University of Chicago Press, 1990 Paper: 978-0-226-10099-9 | Cloth: 978-0-226-10098-2 Library of Congress Classification QB461.C468 1990 Dewey Decimal Classification 523.01

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ABOUT THIS BOOK

This is the fifth of six volumes collecting significant papers of the distinguished astrophysicist and Nobel laureate S. Chandrasekhar. His work is notable for its breadth as well as for its brilliance; his practice has been to change his focus from time to time to pursue new areas of research. The result has been a prolific career full of discoveries and insights, some of which are only now being fully appreciated.

Chandrasekhar has selected papers that trace the development of his ideas and that present aspects of his work not fully covered in the books he has periodically published to summarize his research in each area.

Volume 5 covers all of Chandrasekhar's contributions to the general theory of relativity and relativity's astrophysical applications (except his research on black holes and colliding gravitational waves, which is covered in Volume 6). The major topics include the influence of general relativity on the pulsations and stability of stars; the back reaction of gravitational waves on their sources; and post-Newtonian approximations to general relativity and their astrophysical applications. In addition to research papers, the volume includes two 1972 lectures in which Chandrasekhar assessed the past, present, and future of relativistic astrophysics. The foreword by astrophysicist Kip S. Thorne is an absorbing, brief history of the field since 1961, capturing the atmosphere of the early research and clarifying Chandrasekhar's dominant role in it.

Chandrasekhar has never written a monograph synthesizing his research in relativistic astrophysics, and therefore this volume of his papers serves as a summary of that work for students and more senior researchers.

TABLE OF CONTENTS

Foreword by Kip S. Thorne

PART ONE

Relativistic Instabilities and Post-Newtonian Approximations

1. Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity Physical Review Letters 12, no. 4 (January 1964): 114-116. Incorporates errata in Physical Review Letters 12, no. 5 (April 1964).

2. The Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity The Astrophysical Journal 140, no. 2 (August 1964): 417-33

3. The Dynamical Instability of the White-Dwarf Configurations Approaching the Limiting Mass. With R. F. Tooper The Astrophysical Journal 139, no. 4 (May 1964): 1396-98

4. The Virial Theorem in General Relativity in the Post-Newtonian Approximation. With G. Contopoulos Proceedings of the National Academy of Sciences 49, no. 5 (May 1963): 608-13

5. On a Post-Galilean Transformation Appropriate to the Post Newtonian Theory of Einstein, Infeld and Hoffman. With G. Contopoulos Proceedings of the Royal Society, A, 298 (April 1967): 123-41

6. The Post-Newtonian Equations of Hydrodynamics in General Relativity The Astrophysical Journal 142, no. 4 (November 1965): 1488-1512

7. Conservation Laws in General Relativity and in the Post Newtonian Approximations The Astrophysical Journal 158, no. 1 (October 1969): 45-54

8. The Second Post-Newtonian Equations of Hydrodynamics in General Relativity. With Yavuz Nutku The Astrophysical Journal 158, no. 1 (October 1969): 55-79

9. The 2-1/2 Post-Newtonian Equations of Hydrodynamics and Radiation Reaction in General Relativity. With F. Paul Esposito The Astrophysical Journal 160, no. 1 (April 1970): 153-79

10. Post-Newtonian Methods and Conservation Laws Relativity, ed. M. Carmeli, S. I. Fickler, and L. Witten
{Plenum Press, 1970),81-108

11. The Stability of Gaseous Masses for Radial and Non-Radial Oscillations in the Post-Newtonian Approximation of General Relativity The Astrophysical Journal 142, no. 4 (November 1965): 1519-40

12. On the Onset of Relativistic Instability in Highly Centrally Condensed Stars. With Norman R. Lebovitz Monthly Notices of the Royal Astronomical Society 207, no. 2 (March 1984): 13p-16p

13. Solutions of Two Problems in the Theory of Gravitational Radiation Physical Review Letters 24, no. 11 (March 1970): 611-15

14. The Effect of Gravitational Radiation on the Secular Stability of the Maclaurin Spheroid The Astrophysical Journal 161 , no. 2 (August 1970): 561-69

15. Proceedings at Meeting of the Royal Astronomical Society The Observatory 92, no. 989 (August 1972): 116-20

16. The Stability of Stellar Masses in General Relativity Proceedings of the First European Astronomical Meeting, Athens,September 4-9, 1972, vol. 3 (Berlin: Springer-Verlag, 1974), 162-65

17. The Stability of Relativistic Systems Gravitational Radiation and Gravitational Collapse, ed. C. DeWitt-Morette {D. Reidel, 1974),63-81

18. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. I, The Maclaurin Spheroids and the Virial Theorem The Astrophysical Journal 142, no. 4 (November 1965): 1513-18

19. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. II, The Deformed Figures of the Maclaurin Spheroids The Astrophysical Journal 147, no. 1 (January 1967): 334-52

20. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. III, The Deformed Figures of the Jacobi Ellipsoids The Astrophysical Journal 148, no. 2 (May 1967): 621-44

21. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. IV, The Roche Model The Astrophysical Journal 148, no. 2 (May 1967): 645-49

22. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. V, The Deformed Figures of the Maclaurin Spheroids (Continued) The Astrophysical Journal 167, no. 3 (August 1971): 447-53

23. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. VI, The Deformed Figures of the Jacobi Ellipsoids (Continued) The Astrophysical Journal 167, no. 3 (August 1971): 455-63

24. The Deformed Figures of the Dedekind Ellipsoids in the Post-Newtonian Approximation to General Relativity. With Donna D. Elbert The Astrophysical Journal 192, no. 3 (September 1974): 731-46.
Incorporates corrections and amplifications in The Astrophysical Journal 220, no. 1 (February 1978).

PART TWO

The Stability and the Equilibrium of Rotating Systems in General Relativity

25. Criterion for the Instability of a Uniformly Rotating Configuration in General Relativity. With John L. Friedman Physical Review Letters 26, no. 17 (April 1971): 1047-50

26. On the Stability of Axisymmetric Systems to Axisymmetric Perturbations in General Relativity. I, The Equations Governing Nonstationary, Stationary, and Perturbed Systems. With John L. Friedman The Astrophysical Journal 175, no. 2 (July 1972): 379-405

27. 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. With John L. Friedman The Astrophysical ]ournaI 176, no. 3 (September 1972): 745-68

28. On the Stability of Axisymmetric Systems to Axisymmetric Perturbations in General Relativity. III, Vacuum Metrics and Carter's Theorem. With John L. Friedman The Astrophysical Journal 177, no. 3 (November 1972): 745-56

29. On the Stability of Axisymmetric Systems to Axisymmetric Perturbations in General Relativity. IV, Allowance for Gravitational Radiation in an Odd-Parity Mode. With John L. Friedman The Astrophysical Journal 181, no. 2 (April 1973): 481-95

30. On a Criterion for the Occurrence of a Dedekind-like Point of Bifurcation Along a Sequence of Axisymmetric Systems. I, Relativistic Theory of Uniformly Rotating Configurations. With John L. Friedman The Astrophysical Journal 185, no. 1 (October 1973): 1-18

31. On a Criterion for the Occurrence of a Dedekind-like Point of Bifurcation Along a Sequence of Axisymmetric Systems. II, Newtonian Theory for Differentially Rotating Configurations. With Norman R. Lebovitz The Astrophysical Journal 185, no. 1 (October 1973): 19-30

32. On a Criterion for the Onset of Dynamical Instability by a Nonaxisymmetric Mode of Oscillation Along a Sequence of Differentially Rotating Configurations The Astrophysical Journal 187, no. 1 (January 1974): 169-74

33. Virial Relations for Uniformly Rotating Fluid Masses in General Relativity The Astrophysical Journal 147, no. 1 (January 1967): 383-84

34. On the Slowly Rotating Homogeneous Masses in General Relativity. With John C. Miller Monthly Notices ofthe Royal Astronomical Society 167, no. 1 (April 1974): 63-79

PART THREE

Miscellaneous Papers in General Relativity

35. A Limiting Case of Relativistic Equilibrium General Relativity (Papers in Honor of J. L. Synge), ed.
L. O'Raifeartaigh (Oxford: Clarendon Press, 1972), 185-99

36. The Geodesics in Godel's Universe. With James P. Wright Proceedings ofthe National Academy of Sciences 48, no. 3
(March 1961): 341-47

37. On the "Derivation" of Einstein's Field Equations American Journal of Physics 40, no. 2 (February 1972): 224-34

38. The General Theory of Relativity: The First Thirty Years Contemporary Physics 21, no. 5 (1980): 429-49

39. The Increasing Role of General Relativity in Astronomy (Halley Lecture for 1972) The Observatory 92, no. 990 (October 1972): 160-74

40. Einstein's General Theory of Relativity and Cosmology The Great Ideas Today (Encyclopaedia Britannica, 1979),90-138

A Commentary on Dirac's Views on lithe Excellence of General Relativity" Festi-Val: Festschrift for Val Telegdi, ed K. Winter (Amsterdam: North Holland, 1988),49-56

REQUEST ACCESSIBLE FILE

If you are a student who has a disability that prevents you
from using this book in printed form, BiblioVault may be able to supply you
with an electronic file for alternative access.

Please have the disability coordinator at your school fill out this form.

University of Chicago Press, 1990 Paper: 978-0-226-10099-9 Cloth: 978-0-226-10098-2

This is the fifth of six volumes collecting significant papers of the distinguished astrophysicist and Nobel laureate S. Chandrasekhar. His work is notable for its breadth as well as for its brilliance; his practice has been to change his focus from time to time to pursue new areas of research. The result has been a prolific career full of discoveries and insights, some of which are only now being fully appreciated.

Chandrasekhar has selected papers that trace the development of his ideas and that present aspects of his work not fully covered in the books he has periodically published to summarize his research in each area.

Volume 5 covers all of Chandrasekhar's contributions to the general theory of relativity and relativity's astrophysical applications (except his research on black holes and colliding gravitational waves, which is covered in Volume 6). The major topics include the influence of general relativity on the pulsations and stability of stars; the back reaction of gravitational waves on their sources; and post-Newtonian approximations to general relativity and their astrophysical applications. In addition to research papers, the volume includes two 1972 lectures in which Chandrasekhar assessed the past, present, and future of relativistic astrophysics. The foreword by astrophysicist Kip S. Thorne is an absorbing, brief history of the field since 1961, capturing the atmosphere of the early research and clarifying Chandrasekhar's dominant role in it.

Chandrasekhar has never written a monograph synthesizing his research in relativistic astrophysics, and therefore this volume of his papers serves as a summary of that work for students and more senior researchers.

TABLE OF CONTENTS

Foreword by Kip S. Thorne

PART ONE

Relativistic Instabilities and Post-Newtonian Approximations

1. Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity Physical Review Letters 12, no. 4 (January 1964): 114-116. Incorporates errata in Physical Review Letters 12, no. 5 (April 1964).

2. The Dynamical Instability of Gaseous Masses Approaching the Schwarzschild Limit in General Relativity The Astrophysical Journal 140, no. 2 (August 1964): 417-33

3. The Dynamical Instability of the White-Dwarf Configurations Approaching the Limiting Mass. With R. F. Tooper The Astrophysical Journal 139, no. 4 (May 1964): 1396-98

4. The Virial Theorem in General Relativity in the Post-Newtonian Approximation. With G. Contopoulos Proceedings of the National Academy of Sciences 49, no. 5 (May 1963): 608-13

5. On a Post-Galilean Transformation Appropriate to the Post Newtonian Theory of Einstein, Infeld and Hoffman. With G. Contopoulos Proceedings of the Royal Society, A, 298 (April 1967): 123-41

6. The Post-Newtonian Equations of Hydrodynamics in General Relativity The Astrophysical Journal 142, no. 4 (November 1965): 1488-1512

7. Conservation Laws in General Relativity and in the Post Newtonian Approximations The Astrophysical Journal 158, no. 1 (October 1969): 45-54

8. The Second Post-Newtonian Equations of Hydrodynamics in General Relativity. With Yavuz Nutku The Astrophysical Journal 158, no. 1 (October 1969): 55-79

9. The 2-1/2 Post-Newtonian Equations of Hydrodynamics and Radiation Reaction in General Relativity. With F. Paul Esposito The Astrophysical Journal 160, no. 1 (April 1970): 153-79

10. Post-Newtonian Methods and Conservation Laws Relativity, ed. M. Carmeli, S. I. Fickler, and L. Witten
{Plenum Press, 1970),81-108

11. The Stability of Gaseous Masses for Radial and Non-Radial Oscillations in the Post-Newtonian Approximation of General Relativity The Astrophysical Journal 142, no. 4 (November 1965): 1519-40

12. On the Onset of Relativistic Instability in Highly Centrally Condensed Stars. With Norman R. Lebovitz Monthly Notices of the Royal Astronomical Society 207, no. 2 (March 1984): 13p-16p

13. Solutions of Two Problems in the Theory of Gravitational Radiation Physical Review Letters 24, no. 11 (March 1970): 611-15

14. The Effect of Gravitational Radiation on the Secular Stability of the Maclaurin Spheroid The Astrophysical Journal 161 , no. 2 (August 1970): 561-69

15. Proceedings at Meeting of the Royal Astronomical Society The Observatory 92, no. 989 (August 1972): 116-20

16. The Stability of Stellar Masses in General Relativity Proceedings of the First European Astronomical Meeting, Athens,September 4-9, 1972, vol. 3 (Berlin: Springer-Verlag, 1974), 162-65

17. The Stability of Relativistic Systems Gravitational Radiation and Gravitational Collapse, ed. C. DeWitt-Morette {D. Reidel, 1974),63-81

18. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. I, The Maclaurin Spheroids and the Virial Theorem The Astrophysical Journal 142, no. 4 (November 1965): 1513-18

19. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. II, The Deformed Figures of the Maclaurin Spheroids The Astrophysical Journal 147, no. 1 (January 1967): 334-52

20. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. III, The Deformed Figures of the Jacobi Ellipsoids The Astrophysical Journal 148, no. 2 (May 1967): 621-44

21. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. IV, The Roche Model The Astrophysical Journal 148, no. 2 (May 1967): 645-49

22. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. V, The Deformed Figures of the Maclaurin Spheroids (Continued) The Astrophysical Journal 167, no. 3 (August 1971): 447-53

23. The Post-Newtonian Effects of General Relativity on the Equilibrium of Uniformly Rotating Bodies. VI, The Deformed Figures of the Jacobi Ellipsoids (Continued) The Astrophysical Journal 167, no. 3 (August 1971): 455-63

24. The Deformed Figures of the Dedekind Ellipsoids in the Post-Newtonian Approximation to General Relativity. With Donna D. Elbert The Astrophysical Journal 192, no. 3 (September 1974): 731-46.
Incorporates corrections and amplifications in The Astrophysical Journal 220, no. 1 (February 1978).

PART TWO

The Stability and the Equilibrium of Rotating Systems in General Relativity

25. Criterion for the Instability of a Uniformly Rotating Configuration in General Relativity. With John L. Friedman Physical Review Letters 26, no. 17 (April 1971): 1047-50

26. On the Stability of Axisymmetric Systems to Axisymmetric Perturbations in General Relativity. I, The Equations Governing Nonstationary, Stationary, and Perturbed Systems. With John L. Friedman The Astrophysical Journal 175, no. 2 (July 1972): 379-405

27. 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. With John L. Friedman The Astrophysical ]ournaI 176, no. 3 (September 1972): 745-68

28. On the Stability of Axisymmetric Systems to Axisymmetric Perturbations in General Relativity. III, Vacuum Metrics and Carter's Theorem. With John L. Friedman The Astrophysical Journal 177, no. 3 (November 1972): 745-56

29. On the Stability of Axisymmetric Systems to Axisymmetric Perturbations in General Relativity. IV, Allowance for Gravitational Radiation in an Odd-Parity Mode. With John L. Friedman The Astrophysical Journal 181, no. 2 (April 1973): 481-95

30. On a Criterion for the Occurrence of a Dedekind-like Point of Bifurcation Along a Sequence of Axisymmetric Systems. I, Relativistic Theory of Uniformly Rotating Configurations. With John L. Friedman The Astrophysical Journal 185, no. 1 (October 1973): 1-18

31. On a Criterion for the Occurrence of a Dedekind-like Point of Bifurcation Along a Sequence of Axisymmetric Systems. II, Newtonian Theory for Differentially Rotating Configurations. With Norman R. Lebovitz The Astrophysical Journal 185, no. 1 (October 1973): 19-30

32. On a Criterion for the Onset of Dynamical Instability by a Nonaxisymmetric Mode of Oscillation Along a Sequence of Differentially Rotating Configurations The Astrophysical Journal 187, no. 1 (January 1974): 169-74

33. Virial Relations for Uniformly Rotating Fluid Masses in General Relativity The Astrophysical Journal 147, no. 1 (January 1967): 383-84

34. On the Slowly Rotating Homogeneous Masses in General Relativity. With John C. Miller Monthly Notices ofthe Royal Astronomical Society 167, no. 1 (April 1974): 63-79

PART THREE

Miscellaneous Papers in General Relativity

35. A Limiting Case of Relativistic Equilibrium General Relativity (Papers in Honor of J. L. Synge), ed.
L. O'Raifeartaigh (Oxford: Clarendon Press, 1972), 185-99

36. The Geodesics in Godel's Universe. With James P. Wright Proceedings ofthe National Academy of Sciences 48, no. 3
(March 1961): 341-47

37. On the "Derivation" of Einstein's Field Equations American Journal of Physics 40, no. 2 (February 1972): 224-34

38. The General Theory of Relativity: The First Thirty Years Contemporary Physics 21, no. 5 (1980): 429-49

39. The Increasing Role of General Relativity in Astronomy (Halley Lecture for 1972) The Observatory 92, no. 990 (October 1972): 160-74

40. Einstein's General Theory of Relativity and Cosmology The Great Ideas Today (Encyclopaedia Britannica, 1979),90-138

A Commentary on Dirac's Views on lithe Excellence of General Relativity" Festi-Val: Festschrift for Val Telegdi, ed K. Winter (Amsterdam: North Holland, 1988),49-56

REQUEST ACCESSIBLE FILE

If you are a student who has a disability that prevents you
from using this book in printed form, BiblioVault may be able to supply you
with an electronic file for alternative access.

Please have the disability coordinator at your school fill out this form.