Selected Papers, Volume 6: The Mathematical Theory of Black Holes and of Colliding Plane Waves

by S. Chandrasekhar

University of Chicago Press, 1991 Cloth: 978-0-226-10100-2 | Paper: 978-0-226-10101-9 Library of Congress Classification QB843.B55C483 1991 Dewey Decimal Classification 523.8875

ABOUT THIS BOOK | TOC

ABOUT THIS BOOK

This is the first 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.

TABLE OF CONTENTS

Foreword by Basilis C. Xanthopoulos
Author's Note Part One - The Mathematical Theory of Black Holes 1. The Schwartzschild Black Hole

1. On the Equations Governing the Perturbations of the Schwartzschild Black Hole Proceedings of the Royal Society, A, 343 (1975): 289-98
2. The Quasi-Normal Modes of the Schwartzschild Black Hole. With S. Detweiler Proceedings of the Royal Society, A, 344 (1975): 441-52
3. On the Potential Barriers Surrounding the Schwartzschild Black Hole
Pp. 120-46 in Spacetime and Geometry: The Alfred Schild Lectures, ed. R. A. Matzner and L. C. Shepley. Austin: University of Texas Press, 1982

2. The Kerr Black Hole
4. The Kerr Metric and Stationary Axisymmetric Gravitational Fields Proceedings of the Royal Society, A, 358, (1978): 405-20
5. On the Equations Governing the Axisymmetric Perturbations of the Kerr Black Hole. With S. Detweiler Proceedings of the Royal Society, A, 345 (1975): 145-67
6. On a Transformation of Teukolsky's Equation and the Electromagnetic Perturbations of the Kerr Black Hole Proceedings of the Royal Society, A, 348 (1976): 39-55
7. The Solution of Maxwell's Equations in Kerr Geometry Proceedings of the Royal Society, A, 349 (1976): 1-8
8. The Solution of Dirac's Equation in Kerr Geometry Proceedings of the Royal Society, A, 349 (1976): 571-75
9. On the Reflexion and Transmission of Neutrino Waves by a Kerr Black Hole. With S. Detweiler. Proceedings of the Royal Society, A, 352 (1977): 325-38
10. The Gravitational Perturbation of the Kerr Black Hole.
I. The Perturbations in the Quantities which Vanish in the Stationary State Proceedings of the Royal Society, A, 358 (1978): 421-39
11. The Gravitational Perturbations of the Kerr Black Hole.
II. The Perturbations in the Quantities which are Finite in the Stationary State Proceedings of the Royal Society, A, 358 (1978): 441-65
12. The Gravitational Perturbations of the Kerr Black Hole.
III. Further Amplifications Proceedings of the Royal Society, A, 365 (1979): 425-51
13. The Gravitational Perturbations of the Kerr Black Hole.
IV. The completion of the solution Proceedings of the Royal Society, A, 372 (1980): 475-84

3. The Reissner-Nordström Black Hole
14. On the Equations Governing the Perturbations of the Reissner-Nordström Black Hole Proceedings of the Royal Society, A, 365 (1979): 453-65
15. On the Metric Perturbations of the Reissner-Nordström Black Hole. With B. C. Xanthpoulos Proceedings of the Royal Society, A, 367 (1979): 1-14
16. On One-Dimensional Potential Barriers Having Equal Reflexion and Transmission Coefficients Proceedings of the Royal Society, A, 369 (1980): 425-33
17. On Crossing the Cauchy Horizon of a Reissner-Nordström Black Hole. With J. B. Hartle Proceedings of the Royal Society, A, 384 (1982): 301-15
18. On Algebraically Special Perturbations of Black Holes Proceedings of the Royal Society, A, 392 (1984): 1-13 Part Two - The Mathematical Theory of Colliding Waves
19. On the Nutku-Halil Solution for Colliding Impulsive Gravitational Waves. With V. Ferrari Proceedings of the Royal Society, A, 396 (1984): 55-74
20. On Colliding Waves in the Einstein-Maxwell Theory.
With B. C. Xanthopoulos Proceedings of the Royal Society, A, 398 (1985): 223-59
21. On the Collision of Impulsive Gravitational Waves when Coupled with Fluid Motions. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 402 (1985): 37-65
22. On the Collision of Impulsive Gravitational Waves when Coupled with Null Dust. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 403 (1986): 189-98
23. A New Type of Singularity Created by Colliding Gravitational Waves. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 408 (1986): 175-208
24. On Colliding Waves that Develop Time-like Singularities: A New Class of Solutions of the Einstein-Maxwell Equations. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 410 (1987): 311-36
25. The Effect of Sources on Horizons that May Develop when Plane Gravitational Waves Collid. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 414 (1987): 1-30
26. A Perturbation Analysis of the Bell-Szekeres Space-Time. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 420 (1988): 93-123
27. On Weyl's Solution for Space-Times with Two Commuting Killing Fields Proceedings of the Royal Society, A, 415 (1988): 329-45
28. Some Exact Solutions of Gravitational Waves Coupled with Fluid Motions. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 402 (1985): 205-24

Part Three - Cylindrical Waves
29. Cylindrical Waves in General Relativity Proceedings of the Royal Society, A, 408 (1986): 209-32
30. On the Dispersion of Cylindrical Impulsive Gravitational Waves. With V. Ferrari Proceedings of the Royal Society, A, 412 (1987): 75-91

Part Four - The Two-Center Problem
31. The Two-Centre Problem in General Relativity: The Scattering of Radiation by Two Extreme Reissner-Nordström Black-Holes Proceedings of the Royal Society, A, 421 (1989): 227-58
32. A One-to-One Correspondence between the Static Einstein-Maxwell and Stationary Einstein-Vacuum Space-Times
Proceedings of the Royal Society, A, 423 (1989): 379-86
33. Two Black Holes Attached to Strings. With B. C. Xanthopoulos
Proceedings of the Royal Society, A, 423 (1989): 387-400

Part Five - Additional Papers
34. The Flux Integral For Axisymmetric Perturbations of Static Space-Times. With V. Ferrari Proceedings of the Royal Society, A, 428 (1990): 325-49
35. The Teukolsky-Starobinsky Constant for Arbitrary Spin Proceedings of the Royal Society, A, 430 (1990): 433-38
36. On Stars, Their Evolution and Their Stability. Nobel lecture, 8 December 1983
37. How One May Explore the Physical Content of the General Theory of Relativity
Proceedings of the Yale Symposium in Honor of the 150th anniversary of the birth of J. Willard Gibbs, May 17-19, 1989. The American Mathematical Society and the American Physical Society (1990): 227-51

Selected Papers, Volume 6: The Mathematical Theory of Black Holes and of Colliding Plane Waves

by S. Chandrasekhar

University of Chicago Press, 1991 Cloth: 978-0-226-10100-2 Paper: 978-0-226-10101-9

This is the first 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.

TABLE OF CONTENTS

Foreword by Basilis C. Xanthopoulos
Author's Note Part One - The Mathematical Theory of Black Holes 1. The Schwartzschild Black Hole

1. On the Equations Governing the Perturbations of the Schwartzschild Black Hole Proceedings of the Royal Society, A, 343 (1975): 289-98
2. The Quasi-Normal Modes of the Schwartzschild Black Hole. With S. Detweiler Proceedings of the Royal Society, A, 344 (1975): 441-52
3. On the Potential Barriers Surrounding the Schwartzschild Black Hole
Pp. 120-46 in Spacetime and Geometry: The Alfred Schild Lectures, ed. R. A. Matzner and L. C. Shepley. Austin: University of Texas Press, 1982

2. The Kerr Black Hole
4. The Kerr Metric and Stationary Axisymmetric Gravitational Fields Proceedings of the Royal Society, A, 358, (1978): 405-20
5. On the Equations Governing the Axisymmetric Perturbations of the Kerr Black Hole. With S. Detweiler Proceedings of the Royal Society, A, 345 (1975): 145-67
6. On a Transformation of Teukolsky's Equation and the Electromagnetic Perturbations of the Kerr Black Hole Proceedings of the Royal Society, A, 348 (1976): 39-55
7. The Solution of Maxwell's Equations in Kerr Geometry Proceedings of the Royal Society, A, 349 (1976): 1-8
8. The Solution of Dirac's Equation in Kerr Geometry Proceedings of the Royal Society, A, 349 (1976): 571-75
9. On the Reflexion and Transmission of Neutrino Waves by a Kerr Black Hole. With S. Detweiler. Proceedings of the Royal Society, A, 352 (1977): 325-38
10. The Gravitational Perturbation of the Kerr Black Hole.
I. The Perturbations in the Quantities which Vanish in the Stationary State Proceedings of the Royal Society, A, 358 (1978): 421-39
11. The Gravitational Perturbations of the Kerr Black Hole.
II. The Perturbations in the Quantities which are Finite in the Stationary State Proceedings of the Royal Society, A, 358 (1978): 441-65
12. The Gravitational Perturbations of the Kerr Black Hole.
III. Further Amplifications Proceedings of the Royal Society, A, 365 (1979): 425-51
13. The Gravitational Perturbations of the Kerr Black Hole.
IV. The completion of the solution Proceedings of the Royal Society, A, 372 (1980): 475-84

3. The Reissner-Nordström Black Hole
14. On the Equations Governing the Perturbations of the Reissner-Nordström Black Hole Proceedings of the Royal Society, A, 365 (1979): 453-65
15. On the Metric Perturbations of the Reissner-Nordström Black Hole. With B. C. Xanthpoulos Proceedings of the Royal Society, A, 367 (1979): 1-14
16. On One-Dimensional Potential Barriers Having Equal Reflexion and Transmission Coefficients Proceedings of the Royal Society, A, 369 (1980): 425-33
17. On Crossing the Cauchy Horizon of a Reissner-Nordström Black Hole. With J. B. Hartle Proceedings of the Royal Society, A, 384 (1982): 301-15
18. On Algebraically Special Perturbations of Black Holes Proceedings of the Royal Society, A, 392 (1984): 1-13 Part Two - The Mathematical Theory of Colliding Waves
19. On the Nutku-Halil Solution for Colliding Impulsive Gravitational Waves. With V. Ferrari Proceedings of the Royal Society, A, 396 (1984): 55-74
20. On Colliding Waves in the Einstein-Maxwell Theory.
With B. C. Xanthopoulos Proceedings of the Royal Society, A, 398 (1985): 223-59
21. On the Collision of Impulsive Gravitational Waves when Coupled with Fluid Motions. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 402 (1985): 37-65
22. On the Collision of Impulsive Gravitational Waves when Coupled with Null Dust. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 403 (1986): 189-98
23. A New Type of Singularity Created by Colliding Gravitational Waves. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 408 (1986): 175-208
24. On Colliding Waves that Develop Time-like Singularities: A New Class of Solutions of the Einstein-Maxwell Equations. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 410 (1987): 311-36
25. The Effect of Sources on Horizons that May Develop when Plane Gravitational Waves Collid. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 414 (1987): 1-30
26. A Perturbation Analysis of the Bell-Szekeres Space-Time. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 420 (1988): 93-123
27. On Weyl's Solution for Space-Times with Two Commuting Killing Fields Proceedings of the Royal Society, A, 415 (1988): 329-45
28. Some Exact Solutions of Gravitational Waves Coupled with Fluid Motions. With B. C. Xanthopoulos Proceedings of the Royal Society, A, 402 (1985): 205-24

Part Three - Cylindrical Waves
29. Cylindrical Waves in General Relativity Proceedings of the Royal Society, A, 408 (1986): 209-32
30. On the Dispersion of Cylindrical Impulsive Gravitational Waves. With V. Ferrari Proceedings of the Royal Society, A, 412 (1987): 75-91

Part Four - The Two-Center Problem
31. The Two-Centre Problem in General Relativity: The Scattering of Radiation by Two Extreme Reissner-Nordström Black-Holes Proceedings of the Royal Society, A, 421 (1989): 227-58
32. A One-to-One Correspondence between the Static Einstein-Maxwell and Stationary Einstein-Vacuum Space-Times
Proceedings of the Royal Society, A, 423 (1989): 379-86
33. Two Black Holes Attached to Strings. With B. C. Xanthopoulos
Proceedings of the Royal Society, A, 423 (1989): 387-400

Part Five - Additional Papers
34. The Flux Integral For Axisymmetric Perturbations of Static Space-Times. With V. Ferrari Proceedings of the Royal Society, A, 428 (1990): 325-49
35. The Teukolsky-Starobinsky Constant for Arbitrary Spin Proceedings of the Royal Society, A, 430 (1990): 433-38
36. On Stars, Their Evolution and Their Stability. Nobel lecture, 8 December 1983
37. How One May Explore the Physical Content of the General Theory of Relativity
Proceedings of the Yale Symposium in Honor of the 150th anniversary of the birth of J. Willard Gibbs, May 17-19, 1989. The American Mathematical Society and the American Physical Society (1990): 227-51