Author name code: chandrasekhar
ADS astronomy entries on 2022-09-14
author:"Chandrasekhar, Subrahamanyan" year:1930-1990 
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Title: Book-Review - Selected Papers - Stellar Structure and Stellar
    Atmospheres - Radiative Transfer and Negative Ion of Hydrogen -
    Stochastic Statistical and Hydrodynamic Problems in Physics and
    Astronomy - Plasma Physics Hydrodynamic and Hydromagnetic Stability
    and Application of the Tensor / Virial Theorem - Relativistic
    Astrophysics
Authors: Chandrasekhar, S.
Bibcode: 1990JHA....21..383C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers
Authors: Chandrasekhar, S.
Bibcode: 1990Sci...250..306C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers - V.2 - Radiative Transfer and
    Negative Ion of Hydrogen
Authors: Chandrasekhar, S.; Pagel, B.
Bibcode: 1990Obs...110..136C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers - V.3 - Stochastic Statistical
    and Hydromagnetic Problems in Physics and Astronomy - V.4 - Plasma
    Physics Hydrodynamics and Hydromagnetic Stability and Applications
    of the Tensor Virial Theorem
Authors: Chandrasekhar, S.
Bibcode: 1990Sci...248.1142C
Altcode:
  No abstract at ADS

Title: Science and scientific attitudes
Authors: Chandrasekhar, S.
Bibcode: 1990Natur.344..285C
Altcode:
  On Apollonius, Kepler and Einstein, Newton and Shakespeare, and Madonna
  and Mrs Pelham.

Title: Book-Review - Selected Papers - Plasma Physics Hydrodynamic and
    Hydromagnetic Stability and Applications of the Tensor Virial Theorem
Authors: Chandrasekhar, S.
Bibcode: 1990AstQ....7R.188C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers - Stochastic Statistical and
    Hydromagnetic Problems in Physics and Astronomy
Authors: Chandrasekhar, S.
Bibcode: 1990AstQ....7Q.188C
Altcode:
  No abstract at ADS

Title: Selected papers of S. Chandrasekhar. Volume 5: Relativistic
    astrophysics.
Authors: Chandrasekhar, S.
Bibcode: 1990spc5.book.....C
Altcode:
  This volume presents a collection of papers of S. Chandrasekhar
  published during the years 1963 - 1984 and covers all of Chandrasekhar's
  contributions to the general theory of relativity and to relativity's
  astrophysical applications, except his research on black holes and
  on colliding gravitational waves. The papers included are grouped
  into three parts. Contents: Part I. Relativistic instabilities
  and post-Newtonian approximations. Part II. The stability and
  the equilibrium of rotating systems in general relativity. Part
  III. Miscellaneous papers in general relativity.

Title: Discotic liquid crystals
Authors: Chandrasekhar, S.; Ranganath, G. S.
Bibcode: 1990RPPh...53...57C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers - V.5 - Relativistic Astrophysics
Authors: Chandrasekhar, S.
Bibcode: 1990AstQ....7..252C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers - V.2 - Radiative Transfer and
    Negative Ion of Hydrogen
Authors: Chandrasekhar, S.
Bibcode: 1989S&T....78..491C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers - V.1 - Stellar Structure and
    Stellar Atmospheres
Authors: Chandrasekhar, S.
Bibcode: 1989S&T....78..382C
Altcode:
  No abstract at ADS

Title: Book-Review - Selected Papers - VOL.1 - Stellar Structure
    and Stellar Atmospheres
Authors: Chandrasekhar, S.
Bibcode: 1989Sci...245.1517C
Altcode:
  No abstract at ADS

Title: Selected papers of S. Chandrasekhar. Volume 1: Stellar
    structure and stellar atmospheres.
Authors: Chandrasekhar, S.
Bibcode: 1989spc1.book.....C
Altcode:
  This volume presents a collection of papers of S. Chandrasekhar
  published during the years 1929 - 1945. The criteria for selection are
  essentially two: first, the papers have not been included in any of
  the author's books, and second, the papers treat matters of possible
  historical interest not treated in sufficient detail elsewhere. The
  papers included are grouped into five sections. Contents: Part I. The
  theory of white dwarf stars. Part II. The equilibrium of distorted
  polytropes. Part III. Stellar evolution. Part IV. Integral theorems
  on the equilibrium of a star. Part V. Theory of stellar atmospheres.

Title: Selected papers of S. Chandrasekhar. Volume 4: Plasma physics,
    hydrodynamic and hydromagnetic stability, and applications of the
    tensor-virial theorem.
Authors: Chandrasekhar, S.
Bibcode: 1989spc4.book.....C
Altcode:
  This volume presents a collection of papers of S. Chandrasekhar
  published during the years 1954 - 1971. The papers included are
  grouped into three parts. Contents: Part I. Plasma physics. Part
  II. Hydrodynamic and hydromagnetic stability. Part III. Tensor virial
  theorem and its applications.

Title: Selected papers of S. Chandrasekhar. Volume 2: Radiative
    transfer and negative ion of hydrogen.
Authors: Chandrasekhar, S.
Bibcode: 1989spc2.book.....C
Altcode:
  This volume contains much of S. Chandrasekhar's analysis of
  various transfer problems done primarily in the period 1944 -
  1950. Contents: Part I. Radiative transfer. 1. The method of
  discrete ordinates. 2. Radiative transfer allowing for polarization
  of scattering light. 3. Principles of invariance: the H- and the X-
  and Y-functions. 4. Miscellaneous problems. 5. Review articles. Part
  II. Investigation on the negative ion of hydrogen and of two-electron
  atoms.

Title: Selected papers of S. Chandrasekhar. Volume 3: Stochastic,
    statistical, and hydromagnetic problems in physics and astronomy.
Authors: Chandrasekhar, S.
Bibcode: 1989spc3.book.....C
Altcode:
  This volume presents a collection of papers of S. Chandrasekhar
  published during the years 1941 - 1958. The papers included are
  grouped into four parts. Contents: Part I. Dynamical friction and
  Brownian motion. Part II. Statistical problems in astronomy. Part
  III. Statistical theory of hydrodynamic and hydromagnetic
  turbulence. Part IV. Hydromagnetic problems in astrophysics.

Title: Radiative transfer - a personal account.
Authors: Chandrasekhar, S.
Bibcode: 1989fapi.conf...19C
Altcode:
  Contents: 1. Preliminaries. 2. The solutions for some typical problems
  by the method of discrete ordinates. 3. The equation of transfer
  incorporating the polarization of the radiation field - the problem with
  a constant flux. 4. The general vector equation of transfer in terms
  of Stokes parameters. 5. The impact of Ambartsumian's principles of
  invariance. 6. Solutions of the coupled systems of integral equations
  which follow from the principles of invariance. 7. The polarization
  of the sunlit sky.

Title: To Victor Ambartsumian on his 80th birthday
Authors: Chandrasekhar, S.
Bibcode: 1988Ap.....29..408C
Altcode: 1989Ap.....29..408C
  No abstract at ADS

Title: Book-Review - Truth and Beauty - Aesthetics and Motivations
    in Science
Authors: Chandrasekhar, S.
Bibcode: 1988S&T....76R..46C
Altcode:
  No abstract at ADS

Title: Massless particles from a perfect fluid
Authors: Chandrasekhar, S.
Bibcode: 1988Natur.333..506C
Altcode:
  No abstract at ADS

Title: Book-Review - Truth and Beauty - Aesthetics and Motivations
    in Science
Authors: Chandrasekhar, S.
Bibcode: 1988Sci...240.1807C
Altcode:
  No abstract at ADS

Title: Truth and Beauty - Aesthetics and Motivations in Science
Authors: Chandrasekhar, S.; Bondi, H.
Bibcode: 1988Natur.331..668C
Altcode:
  No abstract at ADS

Title: To Victor Ambartsumian on his 80TH Birthday
Authors: Chandrasekhar, S.
Bibcode: 1988Afz....29....7C
Altcode:
  No abstract at ADS

Title: Book-Review - Eddington - the Most Distinguished Astrophysicist
    of his Time
Authors: Chandrasekhar, S.; Woolley, R.
Bibcode: 1987JHA....18..143C
Altcode:
  No abstract at ADS

Title: Book-Review - Eddington - the Most Distinguished Astrophysicist
    of his Time
Authors: Chandrasekhar, S.
Bibcode: 1987AstQ....5..255C
Altcode:
  No abstract at ADS

Title: On the Collision of Impulsive Gravitational Waves when Coupled
    with Null Dust
Authors: Chandrasekhar, S.; Xanthopoulos, B. C.
Bibcode: 1986RSPSA.403..189C
Altcode: 1986RSLPS.403..189C
  The problem of colliding impulsive gravitational waves is considered
  when the region of space-time, after the instant of collision, is
  filled with a mixture of null dusts moving in opposite directions. The
  extension of the resulting space-time, to regions before the instant
  of collision, shows that null dust follows the leading edges of the
  impulsive waves, and, further, that one can arrange that the space-time
  in these regions is identical with what prevails when a perfect fluid
  with ɛ = p fills the region after the instant of collision. This
  ambiguity in the space-time, after the instant of collision, must be
  traced to an inherent ambiguity in the nature of null dust and its
  relation with a perfect fluid with ɛ = p.

Title: Karl Schwarzschild Lecture: The Aesthetic Base of the General
    Theory of Relativity
Authors: Chandrasekhar, S.
Bibcode: 1986MitAG..67...19C
Altcode:
  Karl Schwarzschild is one of the towering physical scientists of this
  century. The breadth and range of his contributions are staggering:
  they cover the entire range of physics, astronomy, and astrophysics of
  his time. The author considers Schwarzschild's attitude and approach to
  scientific problems, as he can discern them from his published papers;
  especially his solution of the equations of general relativity.

Title: Some Exact Solutions of Gravitational Waves Coupled with
    Fluid Motions
Authors: Chandrasekhar, S.; Xanthopoulos, B. C.
Bibcode: 1985RSPSA.402..205C
Altcode: 1985RSLPS.402..205C
  Some exact solutions of Einstein's equations are found which represent
  the interaction of gravitational waves with a perfect fluid in which the
  velocity of sound equals the velocity of light. These solutions, unlike
  the solutions representing the collision of impulsive gravitational
  waves, are bounded by a space-time singularity and have some resemblance
  to cosmological solutions: every time-like trajectory, extended into
  the past, encounters the singularity. Moreover, in the generic case,
  matter may be considered as being created at the singularity.

Title: On the Collision of Impulsive Gravitational Waves when Coupled
    with Fluid Motions
Authors: Chandrasekhar, S.; Xanthopoulos, B. C.
Bibcode: 1985RSPSA.402...37C
Altcode: 1985RSLPS.402...37C
  An exact solution of Einstein's equations, with a source derived from a
  perfect fluid in which the energy density, ɛ, is equal to the pressure,
  p, is obtained. The solution describes the space-time following the
  collision of plane impulsive gravitational waves and is the natural
  generalization of the Nutku-Halil solution of the vacuum equations, in
  the region of interaction under similar basic conditions. A consistent
  extension of the solution, prior to the instant of collision,
  requires that the fluid in the region of interaction is the direct
  result of a transformation of incident null-dust (i.e. of massless
  particles describing null trajectories). The ultimate result of the
  collision is the development of a space-time singularity, the nature
  of which is strongly dependent on the amplitude and the character of
  the sound waves that are present. The distribution of ɛ that follows
  the collision has many intriguing features. The solution obtained in
  this paper provides the first example of an induced transformation of
  a massless into a massive particle.

Title: Book-Review - the Mathematical Theory of Black-Holes
Authors: Chandrasekhar, S.; Thorne, K. S.
Bibcode: 1985AmJPh..53R1013C
Altcode:
  No abstract at ADS

Title: Book-Review - the Mathematical Theory of Black-Holes
Authors: Chandrasekhar, S.; Thorne, K. S.
Bibcode: 1985AmJPh..53Q1013C
Altcode:
  No abstract at ADS

Title: Book-Review - Eddington - the Most Distinguished Astrophysicist
    of his Time
Authors: Chandrasekhar, S.; Whitrow, G. J.
Bibcode: 1985Obs...105...16C
Altcode:
  No abstract at ADS

Title: Book-Review - the Mathematical Theory of Black-Holes
Authors: Chandrasekhar, S.; Gottlober, S.
Bibcode: 1985AN....306..128C
Altcode:
  No abstract at ADS

Title: On stars, their evolution and their stability.
Authors: Chandrasekhar, S.
Bibcode: 1985UsFiN.145..489C
Altcode:
  No abstract at ADS

Title: Book-Review - Eddington - the Most Distinguished Astrophysicist
    of his Time
Authors: Chandrasekhar, S.
Bibcode: 1985S&T....69...34C
Altcode:
  No abstract at ADS

Title: Book-Review - Eddington
Authors: Chandrasekhar, S.; Ronan, C. A.
Bibcode: 1984JBAA...95Q..42C
Altcode:
  No abstract at ADS

Title: Obituary - Hopkins, Jeanne 1923-1984
Authors: Chandrasekhar, S.
Bibcode: 1984S&T....68..492C
Altcode:
  No abstract at ADS

Title: On Stars, Their Evolution and Their Stability
Authors: Chandrasekhar, S.
Bibcode: 1984Sci...226..497C
Altcode:
  The present investigation represents an attempt to show that, in a
  limited sense, the basic facts concerning stars can be understood as
  simply as atoms, taking into account an understanding of atoms in
  terms of two combinations of natural constants. It is pointed out
  that the most important fact concerning a star is its mass, which
  is measured in units of the mass of the sun. The current theories of
  stellar structure and stellar evolution derive their successes largely
  from the fact that a certain combination of the dimensions of a mass
  provides a correct measure of stellar masses. Attention is given to
  the role of radiation pressure, the degeneracy of the electrons in
  white-dwarf stars, the theory of the white-dwarf stars and the limiting
  mass, the conditions under which normal stars develop degenerate cores,
  the evolution of massive stars and the onset of gravitational collapse,
  and the mathematical theory of black holes.

Title: On the Nutku-Halil Solution for Colliding Impulsive
    Gravitational Waves
Authors: Chandrasekhar, S.; Ferrari, V.
Bibcode: 1984RSPSA.396...55C
Altcode: 1984RSLPS.396...55C
  The equations appropriate for space-times with two space-like
  Killing-vectors are set up, ab initio, and explicit expressions for
  the components of the Riemann, the Ricci, and the Einstein tensors in
  a suitable tetrad-frame are written. The equations for the vacuum are
  reduced to a single equation of the Ernst type. It is then shown that
  the simplest linear solution of the Ernst equation leads directly to
  the Nutku-Halil solution for two colliding impulsive gravitational
  waves with uncorrelated polarizations. Thus, in some sense, the
  Nutku-Halil solution occupies the same place in space-times with two
  space-like Killing-vectors as the Kerr solution does in space-times
  with one time-like and one space-like Killing-vector. The Nutku-Halil
  solution is further described in a Newman-Penrose formalism; and the
  expressions for the Weyl scalars, in particular, make the development
  of curvature singularities manifest. Finally, a theorem analogous to
  Robinson's theorem (but much less strong) is proved for space-times
  with two space-like Killing-vectors.

Title: Book-Review - Eddington - the Most Distinguished Astrophysicist
    of his Time
Authors: Chandrasekhar, S.
Bibcode: 1984Sci...224.1364C
Altcode:
  No abstract at ADS

Title: On stars, their evolution and their stability
Authors: Chandrasekhar, S.
Bibcode: 1984RvMP...56..137C
Altcode:
  No abstract at ADS

Title: The general theory of relativity - Why 'It is probably the
    most beautiful of all existing theories'
Authors: Chandrasekhar, S.
Bibcode: 1984JApA....5....3C
Altcode:
  An attempt is made to objectively evaluate the frequent judgment
  of Einstein's general theory of relativity, by such distinguished
  physicists as Pauli (1921), Dirac, Born, and Rutherford, as 'beautiful'
  and 'a work of art'. The criteria applied are that of Francis Bacon
  ('There is no excellent beauty that hath not some strangeness in the
  proportions') and that of Heisenberg ('Beauty is the proper conformity
  of the parts to one another and to the whole'). The strangeness in
  the proportions of the theory of general relativity consists in its
  relating, through juxtaposition, the concepts of space and time and
  those of matter and motion; these had previously been considered
  entirely independent. The criterion of 'conformity' is illustrated
  through the directness with which the theory allows the description
  of black holes.

Title: On the onset of relativistic instability in highly centrally
    condensed stars
Authors: Chandrasekhar, S.; Lebovitz, N. R.
Bibcode: 1984MNRAS.207P..13C
Altcode:
  It is shown that, along the polytropic sequence, the criterion for
  relativistic instability due to radial perturbation can be written to
  less than 3 percent accuracy in where the adiabatic constant is close
  to 4/3. This criterion is expected to indicate when the relativistic
  instability will become relevant for highly centralized condensed stars
  like those in the late stages of stellar evolution when elements of
  higher atomic number are being synthesized.

Title: On Algebraically Special Perturbations of Black Holes
Authors: Chandrasekhar, S.
Bibcode: 1984RSPSA.392....1C
Altcode: 1984RSLPS.392....1C
  Algebraically special perturbations of black holes excite gravitational
  waves that are either purely ingoing or purely outgoing. Solutions,
  appropriate to such perturbations of the Kerr, the Schwarzschild,
  and the Reissner-Nordstrom black-holes, are obtained in explicit forms
  by different methods. The different methods illustrate the remarkable
  inner relations among different facets of the mathematical theory. In
  the context of the Kerr black-hole they derive from the different
  ways in which the explicit value of the Starobinsky constant emerges,
  and in the context of the Schwarzschild and the Reissner-Nordstrom
  black-holes they derive from the potential barriers surrounding them
  belonging to a special class.

Title: Book-Review - Eddington - the Most Distinguished Astrophysicist
    of his Time
Authors: Chandrasekhar, S.
Bibcode: 1984JBAA...94...93C
Altcode:
  No abstract at ADS

Title: Book-Review - the Mathematical Theory of Black-Holes
Authors: Chandrasekhar, S.; King, A.
Bibcode: 1984Obs...104...39C
Altcode:
  No abstract at ADS

Title: Book-Review - Eddington - the Most Distinguished Astrophysicist
    of his Time
Authors: Chandrasekhar, S.; Hoyle, F.
Bibcode: 1984Natur.307Q.575C
Altcode:
  No abstract at ADS

Title: Book-Review - the Mathematical Theory of Black-Holes
Authors: Chandrasekhar, S.
Bibcode: 1984S&T....67Q.428C
Altcode:
  No abstract at ADS

Title: The mathematical theory of black holes.
Authors: Chandrasekhar, S.
Bibcode: 1984grg..conf....5C
Altcode:
  This discussion of the mathematical theory of black holes is restricted
  to features of the theory that reveal its richness. The mathematical
  properties that are examined derive from a consideration of the
  perturbations of black holes. Particular attention is given to the
  problem of the reflection and transmission of incident gravitational
  waves by the Schwarzschild black hole; the Kerr space-time; and the
  Reissner-Nordstrom solution.

Title: Book-Review - Eddington
Authors: Chandrasekhar, S.
Bibcode: 1984AExpr...1...42C
Altcode:
  No abstract at ADS

Title: Book-Review - Eddington
Authors: Chandrasekhar, S.
Bibcode: 1984AExpr...1S..39C
Altcode:
  No abstract at ADS

Title: Book-Review - the Mathematical Theory of Black-Holes
Authors: Chandrasekhar, S.; Penrose, R.
Bibcode: 1983Natur.306..404C
Altcode:
  No abstract at ADS

Title: The Mathematical Theory of Black Holes
Authors: Chandrasekhar, S.
Bibcode: 1983grg1.conf....6C
Altcode:
  No abstract at ADS

Title: The mathematical theory of black holes
Authors: Chandrasekhar, S.
Bibcode: 1983mtbh.book.....C
Altcode: 1983QB843.B55C48...
  A detailed treatment of the mathematical theory of black holes is
  presented. The analytical methods on which the theory is based are
  reviewed, and a space-time of sufficient generality to encompass
  the different situations arising in the study of black holes is
  developed. The Schwarzschild space-time and the perturbations of the
  Schwarzschild black hole are addressed. The Reissner-Nordstrom solution,
  the Kerr metric, geodesics in Kerr space-time, electromagnetic waves
  in Kerr geometry, gravitational perturbations of the Kerr black hole,
  and spin-1/2 particles in Kerr geometry are discussed. Other solution
  and methods are examined.

Title: The Highly Collapsed Configurations of a Stellar Mass
Authors: Chandrasekhar, S.
Bibcode: 1982blho.book...25C
Altcode:
  No abstract at ADS

Title: On Crossing the Cauchy Horizon of a Reissner-Nordstrom
    Black-Hole
Authors: Chandrasekhar, S.; Hartle, J. B.
Bibcode: 1982RSPSA.384..301C
Altcode: 1982RSLPS.384..301C
  The behaviour, on the Cauchy horizon, of a flux of gravitational
  and/or electromagnetic radiation crossing the event horizon of a
  Reissner-Nordstrom black-hole is investigated as a problem in the theory
  of one-dimensional potential-scattering. It is shown that the flux of
  radiation received by an observer crossing the Cauchy horizon, along
  a radial time-like geodesic, diverges for all physically reasonable
  perturbations crossing the event horizon, even including those with
  compact support.

Title: On the Potential Barriers Surrounding the Schwarzschild
    Black-Hole
Authors: Chandrasekhar, S.
Bibcode: 1982sag..conf..120C
Altcode:
  No abstract at ADS

Title: Achievements in Astronomy. (Book Reviews: Oort and the
    Universe)
Authors: Chandrasekhar, S.
Bibcode: 1981Sci...211..272V
Altcode:
  No abstract at ADS

Title: Achievements in Astronomy. (Book Reviews: Oort and the
    Universe)
Authors: Chandrasekhar, S.
Bibcode: 1981Sci...211..272C
Altcode:
  No abstract at ADS

Title: The Gravitational Perturbations of the Kerr Black Hole. IV. The
    Completion of the Solution
Authors: Chandrasekhar, S.
Bibcode: 1980RSPSA.372..475C
Altcode:
  This paper eliminates the last remaining lacuna in the information
  that was needed to make the solution for the perturbations in the
  metric coefficients of the Kerr space-time fully explicit. The
  requisite information is obtained from a pair of equations which is
  complementary to the one considered in paper III; and the solution
  of the Newman-Penrose equations governing the perturbations is, thus,
  completed.

Title: The general theory of relativity - The first thirty years
Authors: Chandrasekhar, S.
Bibcode: 1980ConPh..21..429C
Altcode:
  The principal landmarks in the development of general relativity
  (exclusive of cosmology) during the first 30 years after its founding
  are reviewed. Consideration is given to experimental and observational
  verifications of the predictions of the general theory of relativity,
  the post-Newtonian approximation, and Schwarzschild's solution
  for the space-time metric outside a central spherically symmetric
  distribution of mass (the Schwarszchild black hole). Other problems
  discussed include the relativistic equations of hydrostatic equilibrium
  for spherically symmetric distribution of masses and the problem of
  gravitational collapse.

Title: Evidence for a Large Population of Shocked Interstellar Clouds
Authors: Chandrasekhar, S.
Bibcode: 1980JApA....1...33C
Altcode:
  Reprinting of an invited discourse delivered by the author at the
  Seventeenth General Assembly of the International Astronomical Union
  held at Montreal, Canada.

Title: The 1979 Milne Lecture - Milne, Edward-Arthur and the
    Development of Modern Astrophysics
Authors: Chandrasekhar, S.
Bibcode: 1980QJRAS..21...93C
Altcode:
  No abstract at ADS

Title: On One-Dimensional Potential Barriers Having Equal Reflexion
    and Transmission Coefficients
Authors: Chandrasekhar, S.
Bibcode: 1980RSPSA.369..425C
Altcode: 1980RSLPS.369..425C
  Based on the results of earlier studies on the perturbations of the
  Schwarzschild and the Reissner-Nordstrom black holes, it is shown that
  there exists a very general class of potential pairs (V^(+) and V^(-))
  which yield the same reflexion and transmission coefficients. It
  is further shown that these potentials, V^(+) and V^(-), satisfy an
  infinite hierarchy of integral equalities which are, formally, the same
  as the conserved quantities allowed by the Korteweg-deVries equation.

Title: The role of general relativity in astronomy - Retrospect
    and prospect
Authors: Chandrasekhar, S.
Bibcode: 1980HiA.....5...45C
Altcode:
  Past confirmations of the general theory of relativity by the three
  classical tests are reviewed, and attention is given to the role which
  general relativity plays in our understanding of the large-scale
  structure of the universe (i.e., in the realm of cosmology). The
  nature of gravitational collapse as a central problem in astronomy
  is discussed along with the author's considered prospects for general
  relativity in astronomy.

Title: On the Metric Perturbations of the Reissner-Nordstrom
    Black Hole
Authors: Chandrasekhar, S.; Xanthopoulos, B. C.
Bibcode: 1979RSPSA.367....1C
Altcode: 1979RSLPS.367....1C
  The two pairs of one-dimensional wave equations which govern the odd
  and the even-parity perturbations of the Reissner-Nordstrom black hole
  are derived directly from a treatment of its metric perturbations. The
  treatment closely parallels the corresponding treatment in the context
  of the Schwarzschild black hole.

Title: Beauty and the quest for beauty in science
Authors: Chandrasekhar, S.
Bibcode: 1979PhT....32g..25C
Altcode:
  No abstract at ADS

Title: The Gravitational Perturbations of the Kerr Black
    Hole. III. Further Amplifications
Authors: Chandrasekhar, S.
Bibcode: 1979RSPSA.365..425C
Altcode: 1979RSLPS.365..425C
  The present paper is devoted to an amplification of the solution of
  the Newman-Penrose equations considered in the two earlier papers
  of this series. The principal amplification consists in showing that
  the function Psi , in terms of which the metric perturbations are most
  simply expressed (and which was thought to require quadratures), besides
  being separable in its variables, is expressible directly in terms of
  the Teukolsky functions (and eliminates the need for quadratures). It
  is further shown that the completion of the solution for the metric
  perturbations requires the consideration of four additional equations
  which follow from four Ricci identities (not hitherto considered); and
  the solution of these equations is found. It is also pointed out that
  while the perturbation in the Weyl scalar, Psi <SUB>2</SUB>, can be set
  equal to zero, it cannot be deduced to be zero. (The contrary statement
  in the earlier paper arose from an error of a factor 2 in one of the
  equations.) Numerical verification of some of the principal equations
  and identities of the theory is provided. An important aspect of the
  analysis contained in this paper is the emergence of several crucial
  identities among the Teukolsky functions which one might despair of
  verifying directly.

Title: On the Equations Governing the Perturbations of the
    Reissner-Nordstrom Black Hole
Authors: Chandrasekhar, S.
Bibcode: 1979RSPSA.365..453C
Altcode: 1979RSLPS.365..453C
  By considering suitable combinations of the Weyl scalars and the spin
  coefficients, the basic equations governing the perturbations of the
  Reissner-Nordstrom black hole, in the Newman-Penrose formalism, are
  decoupled; a fundamental pair of decoupled equations are obtained. It is
  then shown how this pair of decoupled equations can be transformed into
  one dimensional wave equations which are appropriate for describing
  the perturbations of odd and of even parity. A simple relation is
  obtained which will allow derivation of a solution belonging to one
  parity from a solution belonging to the opposite parity. Finally,
  equations are derived in terms of which one can readily ascertain how
  an arbitrary superposition of gravitational and electromagnetic waves,
  incident on the black hole, will be reflected and absorbed.

Title: An introduction to the theory of the Kerr metric and its
    perturbations.
Authors: Chandrasekhar, S.
Bibcode: 1979grec.conf..370C
Altcode:
  No abstract at ADS

Title: The deformed figures of the Dedekind ellipsoids in the
post-Newtonian approximation to general relativity: corrections
    and amplifications.
Authors: Chandrasekhar, S.; Elbert, D. D.
Bibcode: 1978ApJ...220..303C
Altcode:
  Two errors in the analysis of an earlier paper on the same subject are
  corrected. It is found that as a consequence of the corrections, the
  solution to the post-Newtonian equations (appropriate to determining
  the deformed figures of the Dedekind ellipsoid) now diverges at a point
  where the axes of the ellipsoid are in the ratios 1:0.3370:0.2850. In
  addition, the fourth-harmonic oscillations of the Dedekind ellipsoid
  are considered. It is found that it becomes dynamically unstable when
  its axes are in the ratios 1:0.3121:0.2680.

Title: On the linear perturbations of the Schwarzschild and the
    Kerr geometries
Authors: Chandrasekhar, S.
Bibcode: 1978pans.proc..528C
Altcode:
  No abstract at ADS

Title: The Gravitational Perturbations of the Kerr Black Hole. I. The
    Perturbations in the Quantities which Vanish in the Stationary State
Authors: Chandrasekhar, S.
Bibcode: 1978RSPSA.358..421C
Altcode: 1978RSLPS.358..421C
  As a preliminary towards a complete integration of the Newman-Penrose
  equations governing the gravitational perturbations of the Kerr
  black hole, the perturbations in the spin coefficients and in
  the components of the Weyl tensor, which vanish in the stationary
  state, are considered. The manner of treatment of the basic equations
  yields Teukolsky's equations expressed directly in terms of the basic
  derivative operators of the theory and, further, suggests a preferred
  gauge in which two of the components of the Weyl tensor are governed
  by the same equations as a Maxwell field. Various identities and
  relations that are needed in subsequent work are assembled. In two
  appendixes, the solution of Maxwell's equations in Kerr geometry and
  the perturbations of the charged Kerr-Newman black hole are considered.

Title: The Kerr metric and stationary axisymmetric gravitational
    fields
Authors: Chandrasekhar, S.
Bibcode: 1978RSPSA.358..405C
Altcode: 1978RSLPS.358..405C
  A treatment of Einstein's equations governing vacuum gravitational
  fields which are stationary and axisymmetric is shown to divide itself
  into three parts: a part essentially concerned with a choice of gauge
  (which can be chosen to ensure the occurrence of an event horizon
  exactly as in the Kerr metric); a part concerned with two of the basic
  metric functions which in two combinations satisfy a complex equation
  (Ernst's equation) and in one combination satisfies a symmetric pair of
  real equations; and a third part which completes the solution in terms
  of a single ordinary differential equation of the first order. The
  treatment along these lines reveals many of the inner relations which
  characterize the general solutions, provides a derivation of the Kerr
  metric which is direct and verifiable at all stages, and opens an
  avenue towards the generation of explicit classes of exact solutions
  (an example of which is given).

Title: The Gravitational Perturbations of the Kerr Black Hole. II. The
    Perturbations in the Quantities which are Finite in the Stationary
    State
Authors: Chandrasekhar, S.
Bibcode: 1978RSPSA.358..441C
Altcode:
  The present paper completes the integration of the linearized
  Newman-Penrose equations governing the gravitational perturbations
  of the Kerr black hole. The equations which determine the solutions
  are the four (complex) Bianchi identities (not used in part I) and
  the 24 equations which follow from the commutation relations. The
  principal results are (1) the demonstration that the perturbation in
  the Weyl scalar Psi <SUB>2</SUB> must vanish in a gauge in which the
  scalars Psi <SUB>1</SUB> and Psi <SUB>3</SUB> are assumed to vanish
  identically; (2) the determination of the relative normalization of the
  radial functions (left unspecified in part I) through an integrability
  condition. Further, the solution to the integrability condition defines
  a function involving quadratures over Teukolsky's radial and angular
  functions; and it is in terms of this function that the perturbations
  in the metric coefficients are determined.

Title: Why are the stars as they are
Authors: Chandrasekhar, S.
Bibcode: 1978pans.proc....1C
Altcode:
  Astronomical theories under consideration 40 years ago are surveyed with
  reference to the question of why stars possess the characteristics that
  they have. Eddington's (1926) parable of a physicist on a cloudbound
  planet is examined, and its relation to the (1 - beta-asterisk)
  theorem and to the combination (hc/G) to the 3/2 power divided by H
  squared is discussed. Fowler's resolution to Eddington's paradox is
  described with reference to the question of whether the stars have
  enough energy to cool. The theory of degenerate configurations is
  surveyed with attention to the limiting mass. Other topics include a
  criterion for the stage at which stars can develop degenerate cores
  and the minimum mass for gravitational collapse to be possible.

Title: The gravitational perturbations of the Kerr black hole. I. The
    perturbations in the quantities which vanish in the stationary state.
Authors: Chandrasekhar, S.
Bibcode: 1977RSPSA.358..421C
Altcode:
  No abstract at ADS

Title: The gravitational perturbations of the Kerr black hole. II. The
    perturbations in the quantities which are finite in the stationary
    state.
Authors: Chandrasekhar, S.
Bibcode: 1977RSPSA.358..441C
Altcode:
  No abstract at ADS

Title: The Kerr metric and stationary axisymmetric gravitational
    fields.
Authors: Chandrasekhar, S.
Bibcode: 1977RSPSA.358..405C
Altcode:
  No abstract at ADS

Title: The "Black Hole" in Astrophysics
Authors: Chandrasekhar, S.
Bibcode: 1977nass.book..208C
Altcode:
  No abstract at ADS

Title: On the Reflexion and Transmission of Neutrino Waves by a Kerr
    Black Hole
Authors: Chandrasekhar, S.; Detweiler, S.
Bibcode: 1977RSPSA.352..325C
Altcode: 1976RSPSA.352..325C; 1977RSLPS.352..325C
  The equations governing the two-component neutrino are reduced to
  the form of a one-dimensional wave equation. And it is shown how the
  absence of super-radiance (i.e. a reflexion coefficient in excess of
  one) for incident neutrino waves and its manifestation for incident
  electromagnetic and gravitational waves (of suitable frequencies)
  emerge very naturally from the character of the respective potential
  barriers that surround the Kerr black hole.

Title: On the Equations Governing the Gravitational Perturbations
    of the Kerr Black Hole
Authors: Chandrasekhar, S.; Detweiler, S.
Bibcode: 1976RSPSA.350..165C
Altcode: 1976RSLPS.350..165C
  Teukolsky's radial equation governing the general, non-axisymmetric,
  gravitational perturbations of the Kerr black hole is reduced to
  the form of a one-dimensional wave equation by making use of the
  transformation which enables the treatment of the non-axisymmetric
  modes in exactly the same way as the axisymmetric modes.

Title: REVIEW: Liquid crystals
Authors: Chandrasekhar, S.
Bibcode: 1976RPPh...39..613C
Altcode:
  An extended tutorial review article on the physics and properties
  of thermotropic liquid crystals (LX) as examples of mesomorphic
  states. Thermotropic LX (nematic, cholesteric, and smectic LX) are
  contrasted to lyotropic LX in an introductory section. Statistical
  theories of nematic order, the continuum theory of the nematic
  state, properties of cholesteric LX, and properties of smectic LX
  are the main headings. Topics discussed include: electrical and
  magnetic birefringence, Maier-Saupe theory, deformation modes of
  thermotropic LX (splay, twist, bend modes), Frank disclinations,
  electrohydrodynamic (EHD) instabilities, fast turnoff EHD mode, chevron
  patterns of oscillating domains, backflow effects, light scattering,
  thermomechanical coupling, Freedericksz effect, memory effect, and
  transitions between LX states.

Title: Liquid crystals
Authors: Chandrasekhar, S.
Bibcode: 1976RPPh...39..615C
Altcode:
  No abstract at ADS

Title: The Solution of Dirac's Equation in Kerr Geometry
Authors: Chandrasekhar, S.
Bibcode: 1976RSPSA.349..571C
Altcode: 1976RSLPS.349..571C
  Dirac's equation for the electron in Kerr geometry is separated;
  and the general solution is expressed as a superposition of solutions
  derived from a purely radial and a purely angular equation.

Title: The Solution of Maxwell's Equations in Kerr Geometry
Authors: Chandrasekhar, S.
Bibcode: 1976RSPSA.349....1C
Altcode: 1976RSLPS.349....1C
  Explicit solutions for the vector-potential of a vacuum Maxwell-field
  in Kerr geometry are obtained in terms of Teukolsky's radial and
  angular functions.

Title: Astronomers' Petition
Authors: Schramm, David N.; Anders, Edward; Chandrasekhar, S.; Palmer,
   Patrick; Parker, Eugene; Simpson, J. A.
Bibcode: 1976Sci...191.1124S
Altcode:
  No abstract at ADS

Title: On a Transformation of Teukolsky's Equation and the
    Electromagnetic Perturbations of the Kerr Black Hole
Authors: Chandrasekhar, S.
Bibcode: 1976RSPSA.348...39C
Altcode: 1976RSLPS.348...39C
  Teukolsky's equation, governing the perturbations (scalar,
  electromagnetic, and gravitational) of the Kerr black hole, is
  transformed, by a simple change of variables, in a manner such that
  there is formally no difference in the treatments of the axisymmetric
  and the non-axisymmetric modes: the role of 'm' is effectively
  eliminated. By considering in detail the case of electromagnetic
  perturbations we show how, in all cases, the problems can be reduced
  to problems in the theory of penetration of one dimensional potential
  barriers with, however, certain novel features. The phenomenon of
  super-radiance, peculiar to the Kerr metric, emerges, for example,
  in an unexpected guise. The case of scalar perturbations is considered
  briefly in an appendix.

Title: On coupled second harmonic oscillations of the congruent
    Darwin ellipsoids.
Authors: Chandrasekhar, S.
Bibcode: 1975ApJ...202..809C
Altcode:
  The paper develops a general theory of coupled second harmonic
  oscillations (with synchronous oscillations as a special degenerate
  case) of the congruent Darwin ellipsoids. The congruent Darwin
  ellipsoids, in equilibrium, consist of two identical ellipsoids facing
  each other and rotating in circular orbits about their common center
  of mass with a constant angular velocity. The relationship of this
  model to the tidal interactions of a binary system is considered.

Title: On the Equations Governing the Axisymmetric Perturbations of
    the Kerr Black Hole
Authors: Chandrasekhar, S.; Detweiler, S.
Bibcode: 1975RSPSA.345..145C
Altcode: 1975RSLPS.345..145C
  It is shown how Teukolsky's equation, governing the perturbations
  of the Kerr black hole, can be reduced, in the axisymmetric case,
  to a one-dimensional wave equation with four possible potentials. The
  potentials are implicitly, dependent on the frequency; and besides,
  depending on circumstances, they can be complex. In all cases
  (i.e. whether or not the potentials are real or complex), the problem
  of the reflexion and the transmission of gravitational waves by the
  potential barriers can be formulated, consistently, with the known
  conservation laws. It is, further, shown that all four potentials lead
  to the same reflexion and transmission coefficients.

Title: The Quasi-Normal Modes of the Schwarzschild Black Hole
Authors: Chandrasekhar, S.; Detweiler, S.
Bibcode: 1975RSPSA.344..441C
Altcode: 1975RSLPS.344..441C
  The quasi-normal modes of a black hole represent solutions of the
  relevant perturbation equations which satisfy the boundary conditions
  appropriate for purely outgoing (gravitational) waves at infinity
  and purely ingoing waves at the horizon. For the Schwarzschild
  black hole the problem reduces to one of finding such solutions for a
  one-dimensional wave equation (Zerilli's equation) for a potential which
  is positive everywhere and is of short-range. The notion of quasi-normal
  modes of such one-dimensional potential barriers is examined with two
  illustrative examples; and numerical solutions for Zerilli's potential
  are obtained by integrating the associated Riccati equation.

Title: On the Equations Governing the Perturbations of the
    Schwarzschild Black Hole
Authors: Chandrasekhar, S.
Bibcode: 1975RSPSA.343..289C
Altcode:
  A coherent self-contained account of the equations governing the
  perturbations of the Schwarzschild black hole is given. In particular,
  the relations between the equations of Bardeen &amp; Press, of Zerilli
  and of Regge &amp; Wheeler are explicitly established.

Title: Development of general relativity
Authors: Chandrasekhar, S.
Bibcode: 1974Natur.252...15C
Altcode:
  This article is based on an invited talk given at the 1974 annual
  meeting of the American Physical Society in Chicago on the occasion
  of the award of the Dannie Heineman Prize for Mathematical Physics,
  February 5, 1974. (The substance of this lecture has been published
  for private circulation in the Summer 1974 issue of The University of
  Chicago Magazine.)

Title: The deformed figures of the Dedekind ellipsoids in the
    post-Newtonian approximation to general relativity.
Authors: Chandrasekhar, S.; Elbert, D. D.
Bibcode: 1974ApJ...192..731C
Altcode:
  The effects of general relativity, in the post-Newtonian approximation,
  on the Dedekind figures of equilibrium of homogeneous masses are
  determined. It is shown how the post-Newtonian figures can be obtained
  by first altering the velocity field in the Dedekind ellipsoid
  appropriately, and then subjecting it to a suitable Lagrangian
  displacement cubic in the coordinates. The solution exhibits a
  singularity at a point where the axes of the Dedekind ellipsoid are in
  the ratios 1:0.6158:0.4412. However, in contrast to what happens along
  the Jacobian sequence, the occurrence of the singularity along the
  Dedekind sequence is not associated with the onset of any instability
  at that point by a strict Newtonian-like dynamic perturbation.

Title: The Increasing Role of General Relativity in Astronomy
    (Halley Lecture for 1972) [Observatory 92(990), 160, October 1972)]
Authors: Chandrasekhar, S.
Bibcode: 1974SvPhU..17..309C
Altcode:
  No abstract at ADS

Title: On slowly rotating homogeneous masses in general relativity
Authors: Chandrasekhar, S.; Miller, John C.
Bibcode: 1974MNRAS.167...63C
Altcode:
  The present paper is devoted to a study of slowly rotating homogeneous
  masses in which the energy density E is a constant. The structure
  of such configurations is determined with the aid of equations
  derived by Hartle in the exact framework of general relativity. These
  configurations have a natural limit in that the static, non-rotating,
  configurations must have radii (R) exceeding 9/8 times the Schwarzschild
  radius (R5). The derived structures, for varying RiR5, are illustrated
  by a series of graphs. A result of particular interest which emerges
  is that the ellipticity of the configuration, for varying radius but
  constant mass and angular momentum, exhibits a very pronounced maximum
  at RiR5 .

Title: The Stability of Relativistic Systems (invited Paper)
Authors: Chandrasekhar, S.
Bibcode: 1974IAUS...64...63C
Altcode:
  No abstract at ADS

Title: On a Criterion for the Onset of Dynamical Instability by a
    Nonaxisymmetric Mode of Oscillation Along a Sequence of Differentially
    Rotating Configurations
Authors: Chandrasekhar, S.
Bibcode: 1974ApJ...187..169C
Altcode:
  In this paper, a variational base is derived for locating the point
  of onset of dynamical instability along a sequence of differentially
  rotating configurations. The underlying idea is to seek the conditions
  for the existence of quasi-stationary, nonaxisymmetric modes of
  deformation in frames of reference rotating with various preassigned
  angular velocities. Subject headings: hydrodynamics - instabilities
  - rotation

Title: The black hole in astrophysics: the origin of the concept
    and its role.
Authors: Chandrasekhar, S.
Bibcode: 1974ConPh..15....1C
Altcode:
  No abstract at ADS

Title: The Stability of Stellar Masses in General Relativity
Authors: Chandrasekhar, S.
Bibcode: 1974gra..conf..162C
Altcode:
  No abstract at ADS

Title: On a Criterion for the Occurrence of a Dedekind-Like Point of
    Bifurcation Along a Sequence of Axisymmetric Systems. Relativistic
    Theory of Uniformly Rotating Configurations
Authors: Chandrasekhar, S.; Friedman, John L.
Bibcode: 1973ApJ...185....1C
Altcode:
  Stationary nonaxisymmetric systems in general relativity are
  considered. It is shown that the theory of such systems can
  be developed along lines which closely parallel the theory of
  nonstationary axisymmetric systems. Equations are derived which govern
  small nonaxisymmetric departures from equilibrium of axisymmetric
  configurations of perfect fluid in uniform rotation. In terms of these
  equations, the condition that a uniformly rotating configuration will
  allow a quasi-stationary nonaxisymmetric deformation with a -dependence
  of the form e (where m is an integer greater than or equal to one)
  is obtained. A variational principle expressing this condition is also
  derived. Subject headings: relativity - rotation

Title: On a Criterion for the Occurrence of a Dedekind-Like Point of
    Bifurcation Along a Sequence of Axisymmetric Systems. 11. Newtonian
    Theory for Differentially Rotating Configurations
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1973ApJ...185...19C
Altcode:
  The equations in the Newtonian theory, which govern quasi-stationary
  nonaxisymmetric deformations of axisymmetric configurations in
  nonuniform rotation, are derived; and the condition for the existence
  of such deformations with a -dependence of the form e (where m is
  an integer greater than or equal to 1) is expressed in terms of
  a variational principle. The condition for the case m = 2 applies
  for the occurrence of a Dedekind-like point of bifurcation. In an
  appendix the variational principle governing the axisymmetric modes
  of oscillation of differentially rotating systems is reformulated in a
  manner that avoids the solution of a secondorder partial differential
  equation. Subject heading: rotation

Title: On the Stability of Axisymmetric Systems to Axisymmetric
    Perturbations in General Relativity.IV. Allowance for Gravitational
    Radiation in an Odd-Parity Mode
Authors: Chandrasekhar, S.; Friedman, John L.
Bibcode: 1973ApJ...181..481C
Altcode:
  In the present paper, the variational principle derved in Paper II
  is clarified; and it is shown how it may be used to treat the damping
  of the axisymmetric oscillations of a uniformly rotating star, by the
  emission of gravitational radiation in an odd-parity mode. It is further
  shown that the expression, for the imaginary part of the frequency as
  a surface integral (at infinity), which follows from the variational
  principle, is consistent with the requirements of the conservation of
  energy. Subject headings: gravitation - relativity - rotation

Title: Ellipsoidal figures of equilibrium.
Authors: Chandrasekhar, S.
Bibcode: 1973efe..book.....C
Altcode:
  No abstract at ADS

Title: On the Stability of Axisymmetric Systems to Axisymmetric
    Perturbations in General Relativity. III. Vacuum Metrics and Carter's
    Theorem
Authors: Chandrasekhar, S.; Friedman, John L.
Bibcode: 1972ApJ...177..745C
Altcode:
  The analysis of Paper II is specialized to vacuum metrics appropriately
  for a discussion of their stability. And Carter's theorem, that
  asymptotically fiat axisymmetric vacuum metrics, external to black
  holes, cannot allow nontrivial axisymmetric neutral deformations,
  is deduced.

Title: The increasing role of general relativity in astronomy
Authors: Chandrasekhar, S.
Bibcode: 1972Obs....92..160C
Altcode:
  No abstract at ADS

Title: On the Stability of Axisymmetric Systems to Axisymmetric
    Perturbations in General Relativity. II. a Criterion for the Onset
    of Instability in Uniformly Rotating Configurations and the Frequency
    of the Fundamental Mode in Case of Slow Rotation
Authors: Chandrasekhar, S.; Friedman, John L.
Bibcode: 1972ApJ...176..745C
Altcode:
  The theory developed in Paper I is applied to solve two problems in
  general relativity: to obtain a criterion for the onset of instability
  in a uniformly rotating configuration via a neutral mode of axisymmetric
  oscillation; and to obtain an exact and an explicit formula for
  the square of the frequency of the fundamental axisymmetric mode of
  oscillation of a configuration rotating uniformly but slowly.

Title: On the Stability of Axisymmetric Systems to Axisymmetric
    Perturbations in General Relativity, I. The Equations Governing
    Nonstationary, and Perturbed Systems
Authors: Chandrasekhar, S.; Friedman, John L.
Bibcode: 1972ApJ...175..379C
Altcode:
  Axisymmetric systems in general relativity are considered. The field
  and the fluid equations that are appropriate to general nonstationary
  (but axisymmetric) systems are first derived. They are then specialized
  to yield the equations which govern stationary equilibrium. The
  equations whieh determine the evolution of small departures from
  equilibrium are also obtained. Related matters that are considered
  include the Landau-Lifshitz complex, the conserved quantities, and the
  constancy of the baryon number and the angular momentum (per baryon)
  of a fluid element as it moves. The theory is developed with a view
  toward establishing criteria for the stability of rotating systems to
  axisymmetric perturbations.

Title: INVITED PAPER The Stability of Stellar Configurations in
    General Relativity.
Authors: Chandrasekhar, S.
Bibcode: 1972BAAS....4Q.315C
Altcode:
  No abstract at ADS

Title: On the ``Derivation'' of Einstein's Field Equations
Authors: Chandrasekhar, S.
Bibcode: 1972AmJPh..40..224C
Altcode:
  An attempt is made to clarify the physical and the mathematical
  reasonings that underlie Einstein's laws of gravitation. It appears
  that only by a mixture of physical reasonableness, mathematical
  simplicity, and aesthetic sensibility can one arrive at Einstein's field
  equations. The general theory of relativity is in fact an example of
  ``the power of speculative thought.'' The topics considered include a
  discussion of the principle of equivalence and the view of space-time
  as a geometric manifold. Two ``derivations'' of Einstein's equations
  are given: one based on physical reasonableness and the other based
  on a variational principle and mathematical simplicity.

Title: A limiting case of relativistic equilibrium.
Authors: Chandrasekhar, S.
Bibcode: 1972grec.conf..185C
Altcode:
  No abstract at ADS

Title: Some elementary applications of thevirial theorem to stellar
    dynamics
Authors: Chandrasekhar, S.; Elbert, Donna D.
Bibcode: 1972MNRAS.155..435C
Altcode:
  The dynamical evolution of spherical and spheroidal systems of mass
  points is examined with the aid of the scalar and the tensor forms
  of the virial theorem. Spherical systems with positive total energy
  tend to disperse to infinity while those with negative total energy
  execute periodic oscillations of finite amplitude. Spheroidal systems
  with positive total energy exhibit expansion like the spherical systems;
  but they also become less oblate (and sometimes actually become prolate)
  if they are initially oblate, and less prolate if they are initially
  prolate. Spheroidal systems with negative total energy collapse to
  smaller volumes while enhancing their initial oblateness or prolateness.

Title: The Post-Newtonian Effects of General Relativity on the
    Equilibrium of Uniformaly Rotating Bodies.VI. The Deformed Figures
    of the Jacobi Ellipsoids (Continued)
Authors: Chandrasekhar, S.
Bibcode: 1971ApJ...167..455C
Altcode:
  The theory of the (deformed) post-Newtonian Jacobi ellipsoid developed
  in an earlier paper is specialized suitably to make a comparison
  with the Newtonian ellipsoid having the same angular momentum and
  baryon number.

Title: The Post-Newtonian Effects of General Relativity on the
    Equilibrium of Uniformly Rotating Bodies. V. The Deformed Figures
    of the Maclaurin Spheroids (Continued)
Authors: Chandrasekhar, S.
Bibcode: 1971ApJ...167..447C
Altcode:
  The theory of the (deformed) post-Newtonian Maclaurin spheroid developed
  in an earlier paper is specialized suitably to make a comparison
  with the Newtonian spheroid having the same angular momentum and
  baryon number.

Title: Criterion for the Instability of a Uniformly Rotating
    Configuration in General Relativity
Authors: Chandrasekhar, S.; Friedman, John L.
Bibcode: 1971PhRvL..26.1047C
Altcode:
  Uniformly rotating configurations in general relativity are considered,
  and a condition is obtained that they can be quasistatically deformed
  without violating any of the requirements for equilibrium. This
  condition extends, into the domain of the rotating stars, the
  criterion for the onset of dynamical instability (via a neutral mode
  of oscillation) that occurs by radial pulsations in nonrotating stars.

Title: An Announcement for Our Authors
Authors: Chandrasekhar, S.
Bibcode: 1971ApJ...164..397C
Altcode:
  No abstract at ADS

Title: An Announcement for Our Authors
Authors: Chandrasekhar, S.
Bibcode: 1971ApJ...164L..79C
Altcode:
  No abstract at ADS

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1970ApJ...162....1C
Altcode:
  No abstract at ADS

Title: The Evolution of the Jacobi Ellipsoid by Gravitational
    Radiation
Authors: Chandrasekhar, S.
Bibcode: 1970ApJ...161..571C
Altcode:
  The quasi-static evolution of the Jacobi ellipsoid by gravitational
  radiation is determined by integrating the equation that gives the
  rate of dissipation of the angular momentum with the constraint that
  the ellipsoid remains Jacobian at all times. It is found that the
  evolution is in the direction of increasing angular velocity toward
  a non-radiating state at the point of bifurcation with the Maclaurin
  sequence.

Title: The Effect of Gravitational Radiation on the Secular Stability
    of the Maclaurin Spheroid
Authors: Chandrasekhar, S.
Bibcode: 1970ApJ...161..561C
Altcode:
  It is shown that the dissipation of energy by gravitational radiation
  induces (in the manner of viscosity) a secular instability of the
  Maclaurin spheroid at the point of bifurcation where the Jacobian
  sequence branches off. But the mode of oscillation that is made unstable
  by radiation reaction is not the same one that is made unstable by
  viscosity.

Title: The Instability of the Congruent DARWIN Ellipsoids. II
Authors: Chandrasekhar, S.
Bibcode: 1970ApJ...160.1043C
Altcode:
  The resonant oscillations of one of two congruent Darwin ellipsoids,
  forced by the natural oscillations of the other, are considered; and
  the instability of the ellipsoids to synchronous coupled oscillations
  is traced to this resonance.

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1970ApJ...160....1C
Altcode:
  No abstract at ADS

Title: The 2½-POST-NEWTONIAN Equations of Hydrodynamics and Radiation
    Reaction in General Relativity
Authors: Chandrasekhar, S.; Esposito, F. Paul
Bibcode: 1970ApJ...160..153C
Altcode:
  In this paper the equations of hydrodynamics in the 2 '-post-Newtonian
  approximation to general relativity are derived. In this approximation
  all terms of O(c-9) are retained consistently with Einstein's field
  equations; it is also the approximation in which terms representing
  the reaction of the fluid to the emission of gravitational radiation
  by the system first make their appearance. The paper is in four
  parts. In Part I (by S. C.) the lowest-order terms in the metric
  coefficients are derived which are consequences of the imposition
  of the Sommerfeld radiation-condition at infinity. It is shown
  (following an early investigation of Trautman) that these terms
  are of O(c-5) in gss, of O(c-5) in gs , and of O(c-0) in g . Unique
  expressions are bbtained for these terms. They are found to be purely
  of Newtonian origin. In Part II (by S. C. and F. P. E.) the equations
  of motion governing the fluid in the -post-Newtonian approximation are
  derived. In addition to the coefficients already determined, these
  equations depend on a knowledge of the term of O(c-7) in goo. This
  term is determined by an explicit appeal to the field equation. It is
  further shown that this approximation brings no change to the density
  (c2pn5 V - g) and the linear momentum ( a) that are conserved in the
  second post-Newtonian approximation. In Part III (by S. C.) it is
  shown that the terms of O( ) in the equations of motion contribute
  principally to the dissipation of the energy and the angular momentum
  conserved in the second post-Newtonian approximatioP. The rates of
  dissipation of energy and of angular momentum that are predicted
  are in exact agreement with the expectations of the linearized
  theory of gravitational radiation. Finally, in Part IV (by S. C. and
  F. P. E.) the energy, 009 - C9 pit0 V - g, to be associated with the
  221 -post-Newtonian approximation is derived by evaluating the (0,
  0)-component of the Landau-Lifshitz complex and the conserved density
  in the 3v1tost-Newtonian approximation.

Title: Solutions of Two Problems in the Theory of Gravitational
    Radiation
Authors: Chandrasekhar, S.
Bibcode: 1970PhRvL..24..611C
Altcode:
  The evolution of an elongated rotating configuration by gravitational
  radiation and the possibility of a secular instability being induced by
  it are considered in the context of the classical homogeneous figures
  of Maclaurin and Jacobi. The triaxial Jacobian ellipsoid evolves in the
  direction of increasing angular velocity and approaches (exponentially)
  the point of bifurcation where it ceases to radiate. Further, radiation
  reaction does not make the Maclaurin spheroid secularly unstable past
  the point of bifurcation.

Title: Post-Newtonian Methods and Conservation Laws
Authors: Chandrasekhar, S.
Bibcode: 1970rela.conf...81C
Altcode:
  No abstract at ADS

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1969ApJ...158..847C
Altcode:
  No abstract at ADS

Title: Conservation Laws in General Relativity and in the
    Post-Newtonian Approximations
Authors: Chandrasekhar, S.
Bibcode: 1969ApJ...158...45C
Altcode:
  It is shown how the exact conservation laws of general relativity,
  expressed in terms of the symmetric energy-momentum complex of Landau
  and Lifshitz, can be used to determine the various conserved quantities
  in the different post-Newtonian approximations. Particular attention
  is given to the conserved energy which emerges as the integral over
  the whole of space of the difference between the (0,0)-com- ponent
  of the Landau-Lifshitz complex and the energy of the conserved mass
  present. The method is illustrated in the framework of the first
  post-Newtonian equations of hydrodynamics

Title: The Second Post-Newtonian Equations of Hydrodynamics in
    General Relativity
Authors: Chandrasekhar, S.; Nutku, Yavuz
Bibcode: 1969ApJ...158...55C
Altcode:
  No abstract at ADS

Title: The Instability of the Congruent Darwin Ellipsoids
Authors: Chandrasekhar, S.
Bibcode: 1969ApJ...157.1419C
Altcode:
  In this paper a class of synchronous coupled oscillations of the
  congruent Darwin ellipsoids is con- sidered; and it is shown that
  two of the five modes of oscillation belonging to this class excite
  instabilities along the entire Darwin sequence

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1969ApJ...155..371C
Altcode:
  No abstract at ADS

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1968ApJ...154....1C
Altcode:
  No abstract at ADS

Title: The Pulsations and the Dynamical Stability of Gaseous Masses
    in Uniform Rotation
Authors: Chandrasekhar, S.; Lebovitz, N. R.
Bibcode: 1968ApJ...152..267C
Altcode:
  A variational principle, applicable to axisymmetric oscillations
  of uniformly rotating axisymmetric configurations, is established
  On the assumption that the Lagrangian displacement (describing
  the oscillation) at any point is normal to the level surface (of
  constant total potential) through that point, it is shown how the
  variational expression, for the frequencies of oscillation, can be
  reduced to simple quadratures. The reduction is explicitly carried
  out for certain stratifications of special interest. Some new results
  on the oscillations of slowly rotating configurations are included;
  and a number of related observations on their stability are also made

Title: The Virial Equations of the Fourth Order
Authors: Chandrasekhar, S.
Bibcode: 1968ApJ...152..293C
Altcode:
  The virial equations of the fourth order are derived; and the results of
  certain formal developments needed for their practical usefulness are
  also given The equations are then used to locate the neutral points,
  along the Maclaurin and the Jacobian sequences, that belong to the
  fourth harmonics

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1968ApJ...152L...1C
Altcode:
  No abstract at ADS

Title: A tensor virial-equation for stellar dynamics
Authors: Chandrasekhar, S.; Lee, Edward S.
Bibcode: 1968MNRAS.139..135C
Altcode:
  A tensor virial-equation is derived for a system consisting of equal
  mass-points, appropriately for stellar dynamics, by starting with the
  Liouville equation governing an ensemble of such systems in the six
  N-dimensional phase space.

Title: The Post-Newtonian Effects of General Relativity on the
    Equilibrium of Uniformly Rotating Bodies.IV. The Roche Model
Authors: Chandrasekhar, S.
Bibcode: 1967ApJ...148..645C
Altcode:
  In this paper, the Roche model, consisting of a tenuous envelope in
  the field of a central rigidly rotating central mass, is considered
  in the framework of the post-Newtonian equations of hydrodynamics;
  and the effect, in particular, on the critical isobaric surface with
  the lenticular shape is determined.

Title: The Post-Newtonian Effects of General Relativity on the
    Equilibrium of Uniformly Rotating Bodies. III. The Deformed Figures
    of the Jacobi Ellipsoids
Authors: Chandrasekhar, S.
Bibcode: 1967ApJ...148..621C
Altcode:
  The effects of general relativity, in the post-Newtonian approximation,
  on the Jacobian figures of equilibrium of uniformly rotating homogeneous
  masses are determined. It is shown, for example, that the post-Newtonian
  figure is obtained by a deformation of the Jacobi ellipsoid by
  a suitable Lagrangian displacement cubic in the coordinates. The
  solution of the post-Newtonian equations exhibits an indeterminacy at
  the point of bifurcation M2, where the Jacobian sequence branches off
  from the Maclaurin sequence, and a singularity at a point J4, where
  the axes of the Jacobi ellipsoid are in the ratios 1:0 2972:0.2575. The
  indeterminacy in the solution at M2 arises from the fact that at this
  point the Maclaurin spheroid is neutral to an infinitesimal deformation
  proportional to (s , -x2, 0); and the singularity at J4 arises from
  the fact that at this point the Jacobi ellipsoid is unstable to the
  deformation induced by the effects of general relativity.

Title: Editorial Notice
Authors: Chandrasekhar, S.; Clemence, G. M.
Bibcode: 1967ApJ...148..319C
Altcode:
  No abstract at ADS

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1967ApJ...148....1C
Altcode:
  No abstract at ADS

Title: On a Post-Galilean Transformation Appropriate to the
    Post-Newtonian Theory of Einstein, Infeld and Hoffmann
Authors: Chandrasekhar, S.; Contopoulos, G.
Bibcode: 1967RSPSA.298..123C
Altcode:
  It is shown that the line element, which forms the basis of the
  post-Newtonian theory of Einstein, Infeld and Hoffmann for the motion of
  mass points under their mutual gravitational attractions, is invariant
  in form to a certain post-Galilean transformation. It is necessary that
  the transformation, expressed as an expansion in inverse powers of c^2
  (c is the velocity of light), include terms of O(c<SUP>-2</SUP>) in the
  transformation for the spatial coordinate and terms of O(c<SUP>-4</SUP>)
  in the transformation for the time coordinate. Comparison with the
  Lorentz transformation (between two frames in uniform relative motion
  with a velocity V), expanded similarly in inverse powers of c^2,
  shows (1) that the spatial part of the transformation includes the
  Lorentzian terms (up to O(c<SUP>-2</SUP>)) and allows, in addition, an
  arbitrary rotation, a uniform motion, and a shift of the origin (all of
  O(c<SUP>-2</SUP>)) and (2) that the temporal part of the transformation
  includes the Lorentzian terms (up to O(c<SUP>-4</SUP>)) and an
  additional term of purely gravitational origin. It is the presence
  of this last gravitational term that gives to the transformation its
  non-Lorentzian character. For a suitable choice of the constants in
  the post-Galilean transformation, the parameter V can be interpreted
  as a velocity of relative motion between the two frames, even as in the
  Lorentz transformation. The invariance of the form of the line element
  to the transformation ensures that the equations of motion which follow
  are similarly invariant to the transformation. This fact is further
  verified by showing that the Lagrangians in the two frames differ
  by the total derivative of a function. The relations between the ten
  constants of the motion in the two frames are found. And the special
  case when the transformation can be regarded as one appropriate to a
  'centre of mass system' is briefly considered.

Title: Virial Relations for Uniformly Rotating Fluid Masses in
    General Relativity
Authors: Chandrasekhar, S.
Bibcode: 1967ApJ...147..383C
Altcode:
  No abstract at ADS

Title: The Stability of Gaseous Masses in the Post-Newtonian
    Approximation
Authors: Chandrasekhar, S.
Bibcode: 1967rta3.book...74C
Altcode:
  No abstract at ADS

Title: The Post-Newtonian Effects on the Equilibrium of the Maclaurin
    Spheroids
Authors: Chandrasekhar, S.
Bibcode: 1967rta3.book...68C
Altcode:
  No abstract at ADS

Title: The Post-Newtonian Effects of General Relativity on the
    Equilibrium of Uniformly Rotating Bodies. II. The Deformed Figures
    of the Maclaurin Spheroids
Authors: Chandrasekhar, S.
Bibcode: 1967ApJ...147..334C
Altcode:
  The equations of post-Newtonian hydrodynamics are solved appropriately
  for a uniformly rotating homogeneous mass with symmetry about the axis
  of rotation. The post-Newtonian figure is obtained as a deformation
  of the Newtonian Maclaurin spheroid (with semi-axes and , say) by
  a Lagrangian displacement proportional to (2) =a'12( 2Xl 2x2, - ),
  where w denotes the distance from the axis of rotation and x1 and x2
  are the Cartesian coordinates in the equatorial plane. It is shown that
  the equation defining the boundary of the post-Newtonian configuration
  is of the form 2 2 R 5 4 2+-2-t-2S2t(e)--4-22 =0, ai a3 a1 a1 a1 a3
  (e) is a determinate function of the eccentricity e of the Maclaurin
  spheroid and R5 (= 2CM/c2) is the Schwarzschild radius. The function
  S t(e) is tabulated in the paper. Further, the angular velocity of
  rotation of the post-Newtonian configuration differs from that of the
  Maclaurin spheroid by an amount which is also tabulated. The solution
  of the post-Newtonian equations exhibits a singularity at a certain
  eccentricity e*(= 0.985226) of the Maclaurin spheroid. The origin
  of this singularity is that at e* the Maclaurin spheroid allows an
  infinitesimal neutral deformation by a displacement proportional to
  (2); and the Newtonian instability of the Maclaurin spheroid at e*
  is excited by the post-Newtonian effects of general relativity.

Title: The Post-Newtonian Equations of Hydrodynamics in General
    Relativity
Authors: Chandrasekhar, S.
Bibcode: 1967rta3.book...43C
Altcode:
  No abstract at ADS

Title: Editorial Notice
Authors: Chandrasekhar, S.
Bibcode: 1967AJ.....72..452C
Altcode:
  No abstract at ADS

Title: The Equilibrium and the Stability of the Riemann Ellipsoids. II
Authors: Chandrasekhar, S.
Bibcode: 1966ApJ...145..842C
Altcode:
  In this paper we consider ellipsoidal figures of eqmlibnum (of
  semi-axes a,, a,, and a,) of homogeneous masses rotating uniformly
  vith an angular velocity and with internal motions having a uniform
  vorticity (in the rotating frame) in the case that the directions of
  and do not coincide. Riemaun `5 theorem, that in this case and must
  lie in a principal plane of the ellipsoid, is shown to follow from
  a consideiation of the non-diagonal components of the second-order
  tensor-virial theorem. The conditions for equilibrium are also derived;
  and the domains of occupancy of these Riemaun ellipsoids in the (a,/a,,
  a,/a,)-plane (on the assumpt'ons, which entail no loss of generality,
  that fl and have no camponents in the x,-direction and that a, &gt; a,)
  are explicitly specified. It is shown that the eqmlibrium ellipsoids are
  of three types: ellipsoids of type I which occupy the domain 2a1 &gt;
  (a, + a,) and a, &gt; a, &gt; a,; ellipsoids of type II for which a,
  &gt; 2a, and a,/a, (&lt;1) are limited by a locus along which fpdx =
  0; and ellipsoids of type III which occupy the domain limited by 2a,
  &lt; (a, - a,) and a locus along which P, = = 0 and a, &gt; a,. And
  quite generally, it is shown that an ellipsoid, represented by a point
  in the allowed domain of occupancy, is a figure of equilihrium for
  two different states of motion ( , ) and ( t, t); and that the two
  resulting configurations are adjoints of one another in the sense of
  Dedekind's theorem. Ellipsoids of type I may he considered as hranching
  off from the Maclaurin sequence with an odd mode of oscillation
  neutralized at the point of bifurcation by the choice of P, and ,
  ( l, and being zero). And ellipsoids of type III may be nmilarly
  considered as hranching off from the ellipsoids of type S (for which
  the directions of and coincide with the x,-axis) along the curve where
  they are marginally unstable. The stability of the Riemaun ellipsoids
  with respect to oscillations helonging to the second harmonics is also
  investigated. It is first shown that the characteristic frequencies
  of oscillation of an ellipsoid and its adjoint are the same; and
  further that 11 and are allowed proper frequencies. The loci along
  which instability sets in, in the different domains of occupancy, are
  determined. Of particular interest are the facts that all ellipsoids
  of type II are unstable; that along the curve where the ellipsoids of
  type III branch off from ellipsoids of type S, the stability passes
  from the latter to the former; and that among the ellipsoids of type
  I there are some very highly flattened ones that are stable. Several
  statements of Riemaun concerning the stability of these ellipsoids are
  not suhstantiated hy the present detailed investigation. The origin
  of Riemann s errors is clarified in the paper by Lebovitz following
  this one.

Title: Editorial
Authors: Chandrasekhar, S.
Bibcode: 1966ApJ...143....1C
Altcode:
  No abstract at ADS

Title: The Stability of Gaseous Masses for Radial and Non-Radial
    Oscillations in the Post-Newtonian Approximation of General
    Relativity.
Authors: Chandrasekhar, S.
Bibcode: 1965ApJ...142.1519C
Altcode:
  The stability of gaseous masses with respect to radial as well
  as non-radial oscillations is considered in the framework of the
  post-Newtonian equations of hydrodynamics The onset of dynamical
  instability at a radius R determined by a formula of the type 2CM
  K c2 (where K is a constant) is confirmed in case the "ratio of the
  specific heats" = (a log p/a log p) (where the subscript S denotes that
  the derivative is with respect to constant entropy) is a constant. An
  expression for K is derived which does not involve any knowledge of the
  equilibrium configuration beyond the Newtonian framework; and the values
  of K appropriate to the polytropes are also listed. With respect to the
  onset of instability for non-radial oscillations, it is shown that the
  classical criterion of Schwarzschild based on the discriminant S(r)=dP
  pdp dr dr is replaced by one based on the discriminant (r) =S(r)+ (F +
  is;;:;) where His the internal energy (per unit volume) and F is a ratio
  defined by the relation p11 = p/(F - 1). An alternative form for (r),
  namely, (r) =S(r)[1+{' d {} } d } where F3 = 1 + (a log T/a log p),,
  shows that the condition for the occurrence of convective instability
  is unaltered in the post-Newtonian approximation.

Title: The Post-Newtonian Equations of Hydrodynamics in General
    Relativity.
Authors: Chandrasekhar, S.
Bibcode: 1965ApJ...142.1488C
Altcode:
  The standard Eulerian equations of hydrodynamics are generalized to
  take into account, consistently with Einstein's field equations, all
  effects of order 1/c2. It is further shown that these post-Newtonian
  equations allow integrals of motion which are entirely analogous to
  the Newtonian integrals that express the conservation of mass, linear
  momentum, angular momentum, and energy. The continued validity of
  these conservation laws enables a consistent definition of "mass,"
  "momentum," and "energy" in the framework of the post-Newtonian
  theory. Besides the equations of motion, an appropriate tensor form
  of the virial theorem is also derived.

Title: The Post-Newtonian Effects of General Relativity on the
    Equilibrium of Uniformly Rotating Bodies. I. The Maclaurin Spheroids
    and the Virial Theorem.
Authors: Chandrasekhar, S.
Bibcode: 1965ApJ...142.1513C
Altcode:
  The post-Newtonian effects of general relativity on the equilibrium of
  uniformly rotating bodies are considered with the aid of a suitably
  generalized version of the classical tensor virial theorem. An exact
  relation exhibiting the relativistic effects is obtained; and it shows
  that, if the figure of equilibrium is approximated by a spheroid,
  the effect of general relativity is to attribute to the spheroid a
  larger angular velocity than the Newtonian value.

Title: The Equilibrum and the Stability of the Riemann Ellipsoids. I.
Authors: Chandrasekhar, S.
Bibcode: 1965ApJ...142..890C
Altcode:
  Riemann's problem is concerned with the ellipsoidal figures of
  equilibrium of homogeneous masses rotating uniformly with an angular
  velocity and with internal motions having a uniform vorticity in
  the rotating frame. In this paper, the equilibrium and the stability
  of these Riemann ellipsoids are considered in the special case the
  axes of rotation and vorticity coincide with a principal axis of the
  ellipsoid. It is shown that for the case considered (1) the equilibrium
  figures can be delineated into sequences- the Riemann sequences-along
  which the ratio f = / is a constant; (2) an ellipsoid which is a figure
  of equilibrium for some given j is also a figure of equilibrium for
  ft = (ai2 + a22)2/ai2ai2f, where ai and a2 are the semi-axes of the
  ellipsoid in the equatorial plane; (3) the two states of internal
  motion, corresponding to f and ft, lead to configurations which are
  adjoint in the sense of a theorem due to Dedekind; (4) the first
  member of a Riemann sequence is a Maclaurin spheroid which is stable
  in the absence of any dissipative mechanism; (5) from each point
  of the stable part of the Maclaurin sequence two Riemann sequences
  bifurcate; (6) there exist two self-adjoint sequences along which f
  = Jt = + (a12 + ai2) /aia and that limit the domain of the Riemann
  sequences in the (a /ai, ai/ai) = plane; and (7) the bifurcation of
  the Jacobian and the Dedekind sequences from, what is usually called,
  the point of bifurcation is a special case of a much more general
  phenomenon. The stability of the Riemann ellipsoids with respect to
  modes of oscillation belonging to the second and the third harmonics
  is also investigated. With respect to modes of oscillation belonging
  to the second harmonics it is shown that (1) the Riemann ellipsoids
  allow a non-trivial neutral mode of oscillation; (2) the characteristic
  frequencies of oscillation of an ellipsoid and its adjoint are the same;
  (3) the Riemann ellipsoids with f &gt; -2 are stable with respect to
  these modes; and (4) instability by one of these modes arises along the
  sequences forj &lt; -2. With respect to modes of oscillation belonging
  to the third harmonics, it is shown that along all Riemann sequences
  instability first arises by a mode which deforms the ellipsoid into
  a pear-shaped configuration. The points at which instability sets in
  along the different Riemann sequences and the loci, which separate the
  regions of stability from the regions of instability in the domain of
  the Riemann ellipsoids considered, are also determined.

Title: The Equilibrium and the Stability of the Dedekind Ellipsoids.
Authors: Chandrasekhar, S.
Bibcode: 1965ApJ...141.1043C
Altcode:
  Figures ot equilibrium of liquid masses with internal motions of uniform
  vorticity define the Dedekind sequence. It has been known for a long
  time that the Dedekind sequence of stationary ellipsoids is congruent
  to the Jacobian sequence of uniformly rotating ellipsoids. It is shown
  in this paper that the characteristic frequencies of oscillation of a
  Dedekind ellipsoid, belonging to the second harmonics, are identical
  with those of a Jacobi ellipsoid having the same figure; but that the
  points at which instability sets in by a mode of oscillation belonging
  to the third harmonics are different along the two sequences.

Title: Non-Radial Oscillations of Gaseous Masses.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1964ApJ...140.1517C
Altcode:
  In this paper the fundamental frequencies of non-radial oscillations of
  polytropic gas spheres, belonging to spherical harmonics of orders 1 =
  1 and 2, are evaluated, in a "second approximation," by a variational
  method. Also, the value of the ratio of the specific heats is determined
  for which an accidental degeneracy occurs between the fundamental
  modes of radial oscillation and non-radial oscillation belonging to 1
  = 2; it is found that this value of varies from 1 6 for a homogeneous
  compressible sphere to 1 5719 for a polytrope of index n = 3.

Title: Erratum: the Dynamical Instability of Gaseous Masses
    Approaching the Schwarzschild Limit in General Relativity.
Authors: Chandrasekhar, S.
Bibcode: 1964ApJ...140.1342C
Altcode:
  No abstract at ADS

Title: The Equilibrium and the Stability of the DARWIN Ellipsoids.
Authors: Chandrasekhar, S.
Bibcode: 1964ApJ...140..599C
Altcode:
  Darwin's problem is concerned with the equilibrium and the
  stability of synchronously rotating homogeneous masses under their
  mutual gravitational and tidal interactions. The problem is solved
  consistently, in a method of approximation due to Jeans, in two special
  cases: the case when one of the two components is of infinitesimal
  mass compared to the other and the case when the two components are
  of equal mass and congruent. In the former case, the problem insofar
  as the equilibrium and the stability of the infinitesimal mass is
  concerned, is hardly distinguishable from Roche's simpler problem in
  which the distorting mass is treated as a rigid sphere. However, in
  Darwin's formulation, the distorting mass (in the case considered) is
  a Maclaurin spheroid; and a principal result is that Darwin's problem
  has no solution when the eccentricity of the spheroid exceeds a certain
  maximum value (= 0.40504). In the case of the congruent components, the
  maximum angular velocity of orbital rotation, the distance of closest
  approach, and the Roche limit (where the equilibrium ellipsoid can be
  deformed into a neighboring equilibrium ellipsoid by a quasi-static,
  infinitesimal, solenoidal, ellipsoidal displacement), all occur at
  different points along the sequence; and instability, by a mode of
  natural oscillation of either component by itself, sets in at a still
  different point. It appears, moreover, that of the two figures of
  equilibrium one obtains (at each separation) those with the greater
  elongations overlap; all the physically realizable equilibrium
  ellipsoids are therefore stable with respect to their individual
  natural oscillations. The bearing of these results on the concepts of
  "limiting stability" and "partial stability" due to Darwin and Jeans
  is briefly examined.

Title: The Dynamical Instability of Gaseous Masses Approaching the
    Schwarzschild Limit in General Relativity.
Authors: Chandrasekhar, S.
Bibcode: 1964ApJ...140..417C
Altcode:
  In this paper the theory of the infinitesimal, baryon-number conserving,
  adiabatic, radial oscillations of a gas sphere is developed in the
  framework of general relativity. A variational base for determining
  the characteristic frequencies of oscillation is established. It
  provides a convenient method for obtaining sufficient conditions for
  the occurrence of dynamical instability. The principal result of the
  analysis is the demonstration that the Newtonian lower limit T4, for
  the ratio of the specific heats , for insuring dynamical stability
  is increased by effects arising from general relativity; indeed, is
  increased to an extent that, so long as is finite, dynamical instability
  will intervene before a mass contracts to the limiting radius (&gt;2.25
  GM/c2) compatible with hydrostatic equilibrium. Moreover, if should
  exceed only by a small amount, then dynamical instability will occur
  if the mass should contract to the radius Rc = K 4 C2 -3 where K is
  a constant depending, principally, on the density distribution in the
  configuration. The value of the constant K is explicitly evaluated for
  the homogeneous sphere of constant energy density and the polytropes
  of indices n = 1, 2, and 3.

Title: The Dynamical Instability of the White-Dwarf Configurations
    Approaching the Limiting Mass.
Authors: Chandrasekhar, S.; Tooper, Robert F.
Bibcode: 1964ApJ...139.1396C
Altcode:
  No abstract at ADS

Title: Otto Struve, 1897-1963.
Authors: Chandrasekhar, S.
Bibcode: 1964ApJ...139..423C
Altcode:
  No abstract at ADS

Title: A General Variational Principle Governing the Radial and the
    Non-Radial Oscillations of Gaseous Masses.
Authors: Chandrasekhar, S.
Bibcode: 1964ApJ...139..664C
Altcode:
  In this paper a general variational principle, applicable to radial
  as well as non-radial oscillations of gaseous masses, is formulated
  and proved. And it is, further, shown that when the normal modes
  are analyzed in vector spherical harmonics, the variational principle
  requires that the square of the characteristic frequency of oscillation,
  (r2, belonging to a particular spherical harmonic, is stationary
  with respect to simultaneous variations of two independent radial
  functions. A consequence of this result is that ff2 (belonging to
  a particular harmonic) emerges as a characteristic root of a 2 X 2
  matrix. Two simple illustrations of the variational principle are given.

Title: On the ellipsoidal figures of equilibrium of homogeneous masses
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1964ApNr....9..323C
Altcode:
  No abstract at ADS

Title: The Equilibrium and the Stability of the Roche Ellipsoids.
Authors: Chandrasekhar, S.
Bibcode: 1963ApJ...138.1182C
Altcode:
  Roche's problem is concerned with the equilibrium and the stability
  of rotating homogeneous masses which are, further, distorted by
  the constant tidal action of an attendant rigid spherical mass. This
  ancient problem is reconsidered in this paper with the principal oblect
  of determining the stability of the equilibrium configurations (the
  ellipsoids of Roche) by a direct evaluation of their characteristic
  frequencies of oscillation belonging to the second harmonics The
  result of the evaluation is the demonstration that the Roche ellipsoid
  becomes unstable at a point subsequent to the Roche limit where the
  angular velocity of rotation, consistent with equilibrium, attains
  its maximum value. This result requires a revision of the current
  common view regarding the meaning that is to be attached to the Roche
  limit Among related matters which are considered are the following:
  the relationships that exist between the sequences of Roche and those
  of Maclaurin, Jacobi, and Jeans; the exhibition and the isolation of
  the second neutral point (belonging to the third harmonics) along the
  Roche sequences; and the effect of compressibility on the stability of
  the Roche ellipsoids. A result which emerges from these considerations
  is the universal instability of the Jacobi ellipsoids under the least
  tidal action. The methods used in this paper are those derived from
  the virial theorem and its various extensions. The principal results
  are summarized in Section X and are exhibited in Figures 1, 2, and 3.

Title: The Ellipticity of a Slowly Rotating Configuration.
Authors: Chandrasekhar, S.; Roberts, P. H.
Bibcode: 1963ApJ...138..801C
Altcode:
  The second-order virial theorem is used to set upper and lower bounds
  for m/e for a slowly rotating confignration, where m is the ratio of the
  centrifugal acceleration at the equator to the (average) gravitational
  acceleration on its surface and ER is the ellipticity of its slightly
  oblate figure of equilibrium. The bounds obtained are explicitly
  evaluated for the polytropes, for a model consisting of a core and a
  mantle of constant densities, and for a particular model for the earth.

Title: Letter to the Editor: a General Variational Principle Governing
    the Radial and the Non-Radial Oscillations of Gaseous Masses.
Authors: Chandrasekhar, S.
Bibcode: 1963ApJ...138..896C
Altcode:
  No abstract at ADS

Title: Non-Radial Oscillations and Convective Instability of Gaseous
    Masses.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1963ApJ...138..185C
Altcode:
  Modes of non-radial oscillation of gaseous masses belonging to spherical
  harmonics of orders 1 = 1 and 3 are considered on the basis of the
  first- and the third-order virial equations. For an assumed Lagrangian
  displacement of the form = (Li; + Li) (where Li;jk and Lj represent a
  total of twenty-one unspecified constants and cr is the characteristic
  frequency to be determined), the theory predicts the occurrence of
  modes of oscillation of two different types: modes (belonging to 1 =
  3) which are analogous to the Kelvin modes of an incompressible sphere
  and modes (belonging to 1 = 1) which are analogous to those discovered
  by Pekeris for a homogeneous compressible sphere and which exhibit its
  convective instability. For the latter modes, the virial equations lead
  to a characteristic equation for cr2 of degree 2 whose coefficients
  are integrals over the variables of the unperturbed configuration,
  including its superpotential. The theory is applied to the polytropic
  gas spheres, and it is shown that they are convectively unstable
  (for the modes belonging to 1 = 1) if the ratio of the specific
  heats is less than a certain critical value The critical values of
  predicted by the (approximate) theory differ from 1 + 1/n (where n
  is the polytropic index) by less than 1 per cent over the range of n
  (&lt;3.5) considered; the extent of this agreement is a measure of the
  accuracy of the method based on the virial equations and the assumed
  form of the Lagrangian displacement.

Title: The Points of Bifurcation Along the Maclaurin, the Jacobi,
    and the Jeans Sequences.
Authors: Chandrasekhar, S.
Bibcode: 1963ApJ...137.1185C
Altcode:
  The role which the second- and the third-order virial equations
  governing equilibrium can play in isolating points of neutral stability
  along equilibrium sequences is discussed and clarified. It is shown
  that a necessary condition for the occurrence of a neutral point is
  that a non-trivial Lagrangian displacement exists for which the first
  variations of alt of the integral relations (five in the second order
  and fifteen in the third order), provided by the virial equations,
  vanish. By using this condition, it is possible, for example, to
  isolate the point of bifurcation along the Jacobian sequence without
  any prior specification of the nature of the sequence which follows
  bifurcation. As further illustrations of the method, the known points
  of neutral stability along the Maclaurin and the Jeans sequences are
  also derived.

Title: On the Stability of the Jacobi Ellipsoids.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1963ApJ...137.1142C
Altcode:
  In this paper the problem of the small oscillations of the Jacobi
  ellipsoids is solved, and all the characteristic frequencies belonging
  to the second and the third harmonics are found. In particular,
  the variation, along the Jacobian sequence, of the characteristic
  frequency with respect to which the Jacobi ellipsoid becomes unstable
  is exhibited.

Title: The Equilibrium and the Stability of the Jeans Spheroids.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1963ApJ...137.1172C
Altcode:
  The equilibrium and the stability of homogeneous masses distorted
  by the tidal effects of a secondary (of mass M' at a distance R)
  are re-examined on the basis of the second-order virial equations. In
  agreement with known results,it is shown that, under circumstances when
  the figure of equilibrium is a prolate spheroid, there is a maximum
  value of p( - GM'/R3) which is compatible with equilibrium. The
  problem of the small oscillations of these Jeans spheroids is next
  considered. The characteristic frequencies of oscillation belonging to
  the second harmonics are determined both in case the mass is considered
  incompressible and in case it is considered compressible and subject
  to the gas laws governing adiabatic changes. In the former case,
  instability sets in when p attains its maximum value; and in the latter
  case it sets in before that happens.

Title: On the Oscillations of the Maclaurin Spheroid Belonging to
    the Third Harmonics.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1963ApJ...137.1162C
Altcode:
  The characteristic frequencies of oscillation of the Maclaurin spheroid
  belonging to the third harmonics are found Two further points of
  neutral stability, beyond the first at eccentricity e = 0.81267, are
  isolated They occur at e = 0.89926 and e = 0.96937; it is the second
  of these that is the analogue of the point of bifurcation along the
  Jacobian sequence.

Title: On the Oscillations and the Stability of Rotating Gaseous
    Masses. III. The Distorted Polytropes.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1962ApJ...136.1082C
Altcode:
  The theory of the oscillations of rotating gaseous masses, developed
  in an earlier paper of this series, is here applied to determine the
  effect of a small rotation ( on the fundamental modes of oscillation of
  a polytrope. The basis for this application is provided by the theory of
  rotationally distorted polytropes; this theory is reviewed and amplified
  further to include a discussion of the superpotential. The various
  tensors, in terms of which the characteristic frequencies of oscillation
  are expressed, are evaluated for distorted polytropes, appropriately,
  to the first order in . The final results on the effect of rotation
  on the characteristic frequencies are presented in the form of tables.

Title: On the Point of Bifurcation Along the Sequence of the Jacobi
    Ellipsoids.
Authors: Chandrasekhar, S.
Bibcode: 1962ApJ...136.1048C
Altcode:
  In this paper, the known point of bifurcation along the sequence of the
  Jacobi ellipsoids is isolated by a new method based on equilibrium
  considerations only. The method consists in finding an integral
  property (or, more generally, a functional) of the configuration which
  vanishes as a condition of equilibrium. The first variation of such a
  functional will vanish at a point of bifurcation (and only at a point of
  bifurcation) for a Lagrangian displacement which deforms the body from
  the shape it has along an equilibrium sequence to the shape it will
  have in the sequence following bifurcation. For finding a functional
  j with the requisite properties, an equation for the third-order
  virial (namely, fpi# ) is first established. And from an examination
  of the conditions, which follow from this equation, for equilibrium,
  it is found that J= [ +x2Q312+x1( 33 22) ] dx (where , is the tensor
  potential of the gravitational field) has all the necessary properties
  The first variation of j, for the Lagrangian displacement which deforms
  a Jacobi ellipsoid into a pear-shaped object, is then evaluated, and
  it is shown that its vanishing determines the point of bifurcation
  along the Jacobian sequence, in agreement with Darwin's result.

Title: The Potentials and the Superpotentials of Homogeneous
    Ellipsoids.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1962ApJ...136.1037C
Altcode:
  Explicit expressions are found for the various potentials and
  superpotentials of homogeneous ellipsoids

Title: On the Occurrence of Multiple Frequencies and Beats in the
    β Canis Majoris Stars.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1962ApJ...136.1105C
Altcode:
  An explanation is suggested for the occurrence of two nearly
  equal frequencies and associated beats in the light- and in the
  velocity-variations of the p Canis Majoris stars. It is shown that if
  the ratio of the specific heats is 1 6 and the star is rotating, any
  disturbance will excite two normal modes with nearly equal frequencies.

Title: On the Oscillations and the Stability of Rotating Gaseous
    Masses. II. The Homogeneous, Compressible Model.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1962ApJ...136.1069C
Altcode:
  The pulsation frequencies of rotating, gaseous masses of uniform
  density, i.e., of the Maclaurin spheroids, are found as functions of
  the angular momentum H and the ratio of the specific heats . Numerical
  calculations for the pulsation frequencies and normal modes are given
  for = 1.3, 4,1.4, 1.5, 1.6, and . One finds that the value of at which
  dynamical instability sets in is reduced from = 4 by rotation. One also
  finds that, when = 1.6, the normal modes of oscillation one obtains
  in the limit H 0 are both very far from being radial.

Title: On Superpotentials in the Theory of Newtonian
    Gravitation. II. Tensors of Higher Rank.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1962ApJ...136.1032C
Altcode:
  In addition to the tensors considered in the earlier paper, the
  following tensors are defined and studied: jj(x) =G#P(x') x½k'i dx',
  ij;k(X) =Gj{P(x') (XffX'iL(Xi ½) Xk'dx , I x - x' 3 and jm1(x)= (x
  )LX½ X% XJ$ )( 5Xk )( )dx These tensors are useful in problems (such
  as the stability of the Jacobi ellipsoids) in which it is necessary
  to examine the effects of perturbations belonging to the third harmonic.

Title: On the Oscillations and the Stability of Rotating Gaseous
    Masses.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1962ApJ...135..248C
Altcode:
  In this paper the oscillations and the stability of a rotating
  gaseous mass are considered on the basis of an appropriate tensor
  form of the virial theorem. On the assumption that the Lagrangian
  displacement can be expressed in the form = XjrXr (Xjr constants), a
  characteristic equation for X (of order eighteen) is derived from the
  nine integral relations provided by the virial theorem. An examination
  of the roots of this characteristic equation enables the enumeration
  of the properties of all the natural modes of oscillation belonging
  essentially to harmonics not higher than the second. It is shown that
  there are three principal groups among these modes: a group of three
  modes, each of which exhibits a doublet character; a group of two
  modes, one of which becomes neutral at a point where the condition
  for the occurrence of a point of bifurcation is satisfied and both
  of which become overstable at a higher angular velocity; and a group
  which represents the coupling of two modes, one of which is purely
  radial and the other of which is purely non-radial in the absence of
  rotation. In addition to these modes, there are two "trivial" modes,
  one of which is neutral and the other of which has a characteristic
  frequency equal to the angular velocity.

Title: An Interpretation of Double Periods in Beta Canis Majoris
    Stars.
Authors: Chandrasekhar, S.; Lebovitz, N. R.
Bibcode: 1962ApJ...135..305C
Altcode:
  No abstract at ADS

Title: On Super-Potentials in the Theory of Newtonian Gravitation.
Authors: Chandrasekhar, S.; Lebovitz, Norman R.
Bibcode: 1962ApJ...135..238C
Altcode:
  The character of the gravitational equilibrium of bodies in rotation
  and with prevalent magnetic fields depends on the tensor potential,
  4=G})P(x') ( ')( ) dx', lx-x'13 and the associated tensors, ii= $
  iidx and pq;ij= fvPXp% $dX This paper is devoted to a consideration of
  these fundamental tensors It is shown, in particular, that the tensor
  potential can be expressed in the form ii= where is the gravitational
  potential as usually defined and x is a super-potential determined by
  the equation V2x= -2 .

Title: A Theorem on Rotating Polytropes.
Authors: Chandrasekhar, S.
Bibcode: 1961ApJ...134..662C
Altcode:
  No abstract at ADS

Title: Diffuse Reflection by a Semi-Infinite Atmosphere.
Authors: Horak, Henry G.; Chandrasekhar, S.
Bibcode: 1961ApJ...134...45H
Altcode:
  Parallel light of flux density irF0 is incident on a plane-parallel,
  atmosphere which scatters light in accordance with the phase function
  p (c6s 0) = o + i#i (cos 0) + #2 (cos 0). The exact solution for the
  emergent radiation field is found by using the invariance-principle
  method.

Title: The Geodesics in Godel's Universe
Authors: Chandrasekhar, S.; Wright, James P.
Bibcode: 1961PNAS...47..341C
Altcode:
  No abstract at ADS

Title: Diffuse Reflection by a Semi-Infinite Atmosphere.
Authors: Horak, Henry G.; Chandrasekhar, S.
Bibcode: 1961AJ.....66S.286H
Altcode:
  The solution has been obtained for the problem of diffuse reflection
  by a semi-infinite atmosphere which scatters light in accordance with
  the phase function p(cos0) =w9 ~,P,(cos0) ~,P,(cos0), where ~~, W~,
  ~2 are constants and P,, P2 are Legendre polynomials. The albedo, W~,
  can be less than or equal to unity. The solution was obtained by the
  principle-of-invariance method.

Title: Buchbesprechungen über: Three Copernican Treatises- The
    Universe of Light- Radiative Transfer(Ref. A. UNSÖLD)
Authors: Rosen, E.; Bragg, W.; Chandrasekhar, S.
Bibcode: 1961ZA.....51..148R
Altcode:
  No abstract at ADS

Title: The Stability of Non-Dissipative Couette Flow in Hydromagnetics
Authors: Chandrasekhar, S.
Bibcode: 1960PNAS...46..253C
Altcode:
  No abstract at ADS

