# Selected Papers, Volume 6

## The Mathematical Theory of Black Holes and of Colliding Plane Waves

- Contents

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

Publications by S. Chandrasekhar

Corrigenda

**Physical Sciences: **
Astronomy and Astrophysics |
Physics and Astronomy |
Theoretical Physics

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