References
Bardeen, J. M., Press, W. H. 1973,J. Math. Phys.,14, 7.
Belinskii, V. A.,Khalatnikov, I. M., Lifshitz, E. M. 1970,Adv.Phys.,19, 523.
Belinskii, V. A., Khalatnikov, I. M., Lifshitz, E. M. 1972,Soviet Phys. JETP,62, 1606.
Carter, B. 1968 “Hamilton-Jacobi and Schrodinger separable solutions of Einstein’s equations”,Commun. Math. Phys.,10, 280.
Carter, B. 1970. “An axisymmetric black hole has only two degrees of freedom”,Phys. Rev. Lett.,26, 331.
Carter, B., McLenaghan, R. G. 1979, “Generalized total angular momentum operator for the Dirac equation in curved spacetime”,Phys. Rev. D.,19, 1093.
Chandrasekhar, S. 1931, “The maximum mass of ideal white dwarfs”,Astrophys.J.,74, 81.
Chandrasekhar, S. 1975, “On the Equations Governing the Perturbations of the Schwarzschild Black Hole”,Proc. R. Soc. London,A343, 289.
Chandrasekhar, S., Detweiler, S. 1975a, “The Quasi-Normal Modes of the Schwarzschild Black Hole”,Proc. R. Soc. London,A344, 441.
Chandrasekhar, S., Detweiler, S. 1975b, “On the Equations Governing the Axisymmetric Perturbations of the Kerr Black Hole”,Proc. R. Soc. London,A345, 145.
Chandrasekhar, S. 1976a, “On a Transformation of Teukolsky’s Equation and the Electromagnetic Perturbations of the Kerr Black Hole”,Proc. R. Soc. London,A348, 39.
Chandrasekhar, S. 1976b, “The Solution of Maxwell’s Equations in Kerr Geometry”,Proc. R.Soc. London,A349, 571.
Chandrasekhar, S. 1976c, “The Solution of Dirac’s Equation in Kerr Geometry”,Proc. R. Soc. London,A349, 571.
Chandrasekhar, S. 1978a, “The Kerr Metric and Stationary Axisymmetric Gravitational Fields”,Proc. R. Soc. London,A358, 405.
Chandrasekhar, S. 1978b, “The Gravitational Perturbations of the Kerr Black Hole. I.”Proc. R. Soc. London,A358, 421.
Chandrasekhar, S. 1978c, “The Gravitational Perturbations of the Kerr Black Hole. II.”Proc. R. Soc. London,A358, 441.
Chandrasekhar, S. 1979a, “The Gravitational Perturbations of the Kerr Black Hole, m.”Proc. R. Soc. London,A365, 425.
Chandrasekhar, S. 1979b, “On the Equations Governing the Perturbations of the Reissner-Nordström Black Hole”,Proc. R. Soc. London,A365, 453.
Chandrasekhar, S., Xanthopoulos, B. C. 1979, “On the Metric Perturbations of the Reissner-Nordström Black Hole”,Proc. R. Soc. London,A367, 1.
Chandrasekhar, S. 1980, “The Gravitational Perturbations of the Kerr Black Hole. IV. The Completion of the Solution”,Proc. R. Soc. London,A372, 475.
Chandrasekhar, S. 1982, “On the Potential Barriers Surrounding the Schwarzschild Black Hole”,Spacetime and Geometry: The Alfred Schild Lectures, ed. R. A. Matzner & L. C. Shepley, (Sheply, Austin: University of Texas Press).
Chandrasekhar, S., Hartle, J. B. 1982, “On Crossing the Cauchy Horizon of a Reissner Nordström Black Hole”,Proc. R. Soc. London,A384, 301.
Chandrasekhar, S. 1983,The Mathematical Theory of Black Holes, (Oxford; Clarendon Press).
Chandrasekhar, S. 1984, “On Algebraically Special Perturbations of Black Holes”,Proc. R. Soc. London,A392, 1.
Chandrasekhar, S., Ferrari, V. 1984, “On the Nutku-Halil Solution for Colliding Impulsive Gravitational Waves”,Proc. R. Soc. London,A396, 55.
Chandrasekhar, S., Xanthopoulos, B. C. 1985a, “On Colliding Waves in the Einstein-Maxwell Theory”,Proc. R. Soc. London,A398, 223.
Chandrasekhar, S., Xanthopoulos, B. C. 1985b, “On the Collision of Impulsive Gravitational Waves when Coupled with Fluid Motions”Proc. R. Soc. London,A402, 37.
Chandrasekhar, S., Xanthopoulos, B. C. 1986a, “On the Collision of Impulsive Gravitational Waves when Coupled with Null Dust”,Proc. R. Soc. London,A403, 189.
Chandrasekhar, S., Xanthopoulos, B. C. 1986b, “A New Type of Singularity Created by Colliding Gravitational Waves”,Proc. R. Soc. London,A408, 175.
Chandrasekhar, S. 1987Truth and Beauty: Aesthetics and Motivations in Science (The University of Chicago Press).
Chandrasekhar, S., Xanthopoulos, B. C. 1987a, “On Colliding Waves that Develop Time-like Singularities”,Proc. R. Soc. London,A410, 311.
Chandrasekhar, S., Xanthopoulos, B. C. 1987b, “The Effect of Sources on Horizons that may Develop when Plane Gravitational Waves Collide”,Proc. R. Soc. London,A414, 1.
Chandrasekhar, S. 1989, “The Two-Centre Problem in General Relativity: The Scattering of Radiation by Two Extreme Reissner-Nordström Black Holes”,Proc. R. Soc. London,A421, 227.
Chandrasekhar, S., Xanthopoulos B. C. 1989, “Two Black Holes Attached to Strings”,Proc. R. Soc.London,A423, 387.
Chandrasekhar, S. 1990, “The Teukolsky-Starobinsky Constant for Arbitrary Spin”,Proc. R. Soc.,A430, 433.
Chandrasekhar, S., Ferrari, V. 1990, “The Flux Integral for Axisymmetric Perturbations of Static Space-Times”,Proc. R. Soc.,A428, 325.
Chandrasekhar, S. 1992,The Series Paintings of Claude Monet and the Landscape of General Relativity, (Pune: Inter-University Centre for Astronomy and Astrophysics).
Clarke, C. J.S. 1993, “The Analysis of Space-Time Singularities”,Cambridge Lecture Notes in Physics, (Cambridge: Cambridge University Press).
Eddington, A. S. 1924, “A comparison of Whitehead’s and Einstein’s formulas”,Nature,113, 192.
Eddington, A. S. 1946,Fundamental Theory, (Cambridge: Cambridge University Press).
Ernst, F. J. 1968,Phys. Rev.,168, 1415–7.
Geroch, R., Held, A., Penrose, R. 1973, “A spacetime calculus based on pairs of null directions,J. Math. Phys.,14, 874–81.
Hawking, S. W. 1966, “The occurrence of singularities in cosmology”,Proc. R. Soc. (London),A294, 511.
Hawking, S. W. 1972, “Black holes in general relativity”,Comm. Math. Phys.,25, 152.
Hawking, S. W., Ellis, G. F. R. 1973,The Large-Scale Structure of Space-Time, (Cambridge: Cambridge University Press).
Hawking, S. W., Penrose, R. 1970, The singularities of gravitational collapse and cosmology,Proc. R. Soc. (London),A314, 529–548.
Israel, W. 1967, “Event horizons in static vacuum spacetimes”,Phys. Rev.,164, 1776.
Kamran, N., McLenaghan, R. G. 1984, “Separation of variables and symmetry operators for the neutrino and Dirac equations in spacetimes admitting a twoparameter abelian orthogonally transitive isometry group and a pair of shearfree geodesic null c Ongruences”,J. Math. Phys.,25, 1019.
Kerr, R. P. 1963, “Gravitational field of a spinning mass as an example of algebraically special metrics”,Phys. Rev. Lett.,11, 237.
Khan, K. A., Penrose, R. 1971,Nature,229, 185.
Landau, L. 1932, “On the theory of stars”,Phys. Z. Sowjetunion I,285.
LemaÎitre, G. 1933, “L’universe en expansion”,Ann. Soc. Sci. Bruxelles I,A53, 51. (cf. p.82).
Lifshitz, E. M., Khalatnikov, I. M. 1963, “Investigations in relativistic cosmology”, inAdvances in Physics,12, 185.
Mason, L. J., Woodhouse, N. M. J. 1996,Integrability, Self-Duality, and Twistor Theory, (Oxford: Oxford University Press).
McNamara, J. M. 1978a,Proc. R. Soc. London,A358, 499.
McNamara, J. M. 1978b,Proc. R. Soc. London,A364, 121.
Newman, E. T., Couch, E., Chinnapared, K., Exton, A., Prakash, A., Torrence, R. 1965, ”Metric of a rotating charged mass”,J. Math. Phys.,6, 918–9.
Newman, E. T., Penrose, R. 1962, “An approach to gravitational radiation by a method of spin coefficients”,J. Math. Phys.,3, 896 (Errata4, 1963, 998).
Nutku, Y., Halil, M. 1977,Phys. Rev. Lett.,39, 1379.
Oppenheimer, J. R., Snyder, H. 1939, “On continued gravitational contraction”,Phys. Rev.,56, 455–9.
Oppenheimer, J. R., Volkoff, H. 1939, “On massive neutron cores”,Phys. Rev.,55, 374.
Page, D. N. 1976, “Dirac equation around a charged, rotating black hole”,Phys. Rev. D.,14, 1509.
Penrose, R. 1965, “Gravitational collapse and spacetime singularities”,Phys. Rev. Lett.,14, 579.
Penrose, R. 1969, “Gravitational collapse: the role of general relativity,Rivista del Nuovo Cimento”,Numero speciale,1, 252–276.
Penrose, R. 1973,Ann. N.Y. Acad. Sci.,224, 125.
Penrose, R. 1978, “Singularities of Space-Time”, inTheoretical Principles in Astrophysics and Relativity, eds. N. R. Lebowitz, W. H. Reid & P. O. Vandervoort (Chicago: Chicago University Press, Chicago).
Penrose, R. 1979, “Singularities and Time-Asymmetry”, inGeneral Relativity, eds. S. W. Hawking & W. Israel (Cambridge: Cambridge University Press).
Robinson, D. C. 1975,Phys. Rev. Lett.,34, 905.
Regge, T., Wheeler, J. A. W., 1957, “Stability of a Schwarzschild singularity”,Phys. Rev.,108, 1063.
Simpson, M., Penrose, R. 1973,Int. J. Theor. Phys.,7, 183.
Synge, J. L. 1950, “The gravitational field of a particle”,Proc. Irish Acad.,A53, 83.
Teukolsky, S. A. 1973, “Perturbations of a rotating black hole: Fundamental equations for gravitational, electromagnetic, and neutrinofield perturbations”,Astrophys. J.,185, 635.
Walker, M., Penrose, R. 1970, “On quadratic first integrals of the geodesic equations for type 22 spacetimes”,Comm. Math. Phys.,18, 265.
Woodhouse, N. M. J., Mason, L. J. 1988, “The Geroch group and non-Hausdorff twistor spaces”,Nonlinearity,1, 73–114.
Zerilli, F. J. 1970,Phys. Rev. D.,2, 2141.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Penrose, R. Chandrasekhar, black holes, and singularities. J Astrophys Astron 17, 213–231 (1996). https://doi.org/10.1007/BF02702305
Issue Date:
DOI: https://doi.org/10.1007/BF02702305