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Chandrasekhar, black holes, and singularities

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References

  • Bardeen, J. M., Press, W. H. 1973,J. Math. Phys.,14, 7.

    Article  Google Scholar 

  • Belinskii, V. A.,Khalatnikov, I. M., Lifshitz, E. M. 1970,Adv.Phys.,19, 523.

    Article  ADS  Google Scholar 

  • Belinskii, V. A., Khalatnikov, I. M., Lifshitz, E. M. 1972,Soviet Phys. JETP,62, 1606.

    Google Scholar 

  • Carter, B. 1968 “Hamilton-Jacobi and Schrodinger separable solutions of Einstein’s equations”,Commun. Math. Phys.,10, 280.

    MATH  Google Scholar 

  • Carter, B. 1970. “An axisymmetric black hole has only two degrees of freedom”,Phys. Rev. Lett.,26, 331.

    Article  ADS  Google Scholar 

  • Carter, B., McLenaghan, R. G. 1979, “Generalized total angular momentum operator for the Dirac equation in curved spacetime”,Phys. Rev. D.,19, 1093.

    Article  ADS  Google Scholar 

  • Chandrasekhar, S. 1931, “The maximum mass of ideal white dwarfs”,Astrophys.J.,74, 81.

    Article  MATH  ADS  Google Scholar 

  • Chandrasekhar, S. 1975, “On the Equations Governing the Perturbations of the Schwarzschild Black Hole”,Proc. R. Soc. London,A343, 289.

    ADS  Google Scholar 

  • Chandrasekhar, S., Detweiler, S. 1975a, “The Quasi-Normal Modes of the Schwarzschild Black Hole”,Proc. R. Soc. London,A344, 441.

    ADS  Google Scholar 

  • Chandrasekhar, S., Detweiler, S. 1975b, “On the Equations Governing the Axisymmetric Perturbations of the Kerr Black Hole”,Proc. R. Soc. London,A345, 145.

    ADS  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1976b, “The Solution of Maxwell’s Equations in Kerr Geometry”,Proc. R.Soc. London,A349, 571.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1976c, “The Solution of Dirac’s Equation in Kerr Geometry”,Proc. R. Soc. London,A349, 571.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1978a, “The Kerr Metric and Stationary Axisymmetric Gravitational Fields”,Proc. R. Soc. London,A358, 405.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1978b, “The Gravitational Perturbations of the Kerr Black Hole. I.”Proc. R. Soc. London,A358, 421.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1978c, “The Gravitational Perturbations of the Kerr Black Hole. II.”Proc. R. Soc. London,A358, 441.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1979a, “The Gravitational Perturbations of the Kerr Black Hole, m.”Proc. R. Soc. London,A365, 425.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1979b, “On the Equations Governing the Perturbations of the Reissner-Nordström Black Hole”,Proc. R. Soc. London,A365, 453.

    ADS  Google Scholar 

  • Chandrasekhar, S., Xanthopoulos, B. C. 1979, “On the Metric Perturbations of the Reissner-Nordström Black Hole”,Proc. R. Soc. London,A367, 1.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1980, “The Gravitational Perturbations of the Kerr Black Hole. IV. The Completion of the Solution”,Proc. R. Soc. London,A372, 475.

    ADS  Google Scholar 

  • 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).

    Google Scholar 

  • Chandrasekhar, S., Hartle, J. B. 1982, “On Crossing the Cauchy Horizon of a Reissner Nordström Black Hole”,Proc. R. Soc. London,A384, 301.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1983,The Mathematical Theory of Black Holes, (Oxford; Clarendon Press).

    MATH  Google Scholar 

  • Chandrasekhar, S. 1984, “On Algebraically Special Perturbations of Black Holes”,Proc. R. Soc. London,A392, 1.

    ADS  Google Scholar 

  • Chandrasekhar, S., Ferrari, V. 1984, “On the Nutku-Halil Solution for Colliding Impulsive Gravitational Waves”,Proc. R. Soc. London,A396, 55.

    ADS  Google Scholar 

  • Chandrasekhar, S., Xanthopoulos, B. C. 1985a, “On Colliding Waves in the Einstein-Maxwell Theory”,Proc. R. Soc. London,A398, 223.

    ADS  Google Scholar 

  • Chandrasekhar, S., Xanthopoulos, B. C. 1985b, “On the Collision of Impulsive Gravitational Waves when Coupled with Fluid Motions”Proc. R. Soc. London,A402, 37.

    ADS  Google Scholar 

  • Chandrasekhar, S., Xanthopoulos, B. C. 1986a, “On the Collision of Impulsive Gravitational Waves when Coupled with Null Dust”,Proc. R. Soc. London,A403, 189.

    ADS  Google Scholar 

  • Chandrasekhar, S., Xanthopoulos, B. C. 1986b, “A New Type of Singularity Created by Colliding Gravitational Waves”,Proc. R. Soc. London,A408, 175.

    ADS  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • 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.

    ADS  Google Scholar 

  • Chandrasekhar, S., Xanthopoulos B. C. 1989, “Two Black Holes Attached to Strings”,Proc. R. Soc.London,A423, 387.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1990, “The Teukolsky-Starobinsky Constant for Arbitrary Spin”,Proc. R. Soc.,A430, 433.

    ADS  Google Scholar 

  • Chandrasekhar, S., Ferrari, V. 1990, “The Flux Integral for Axisymmetric Perturbations of Static Space-Times”,Proc. R. Soc.,A428, 325.

    ADS  Google Scholar 

  • Chandrasekhar, S. 1992,The Series Paintings of Claude Monet and the Landscape of General Relativity, (Pune: Inter-University Centre for Astronomy and Astrophysics).

    Google Scholar 

  • Clarke, C. J.S. 1993, “The Analysis of Space-Time Singularities”,Cambridge Lecture Notes in Physics, (Cambridge: Cambridge University Press).

    Google Scholar 

  • Eddington, A. S. 1924, “A comparison of Whitehead’s and Einstein’s formulas”,Nature,113, 192.

    Google Scholar 

  • Eddington, A. S. 1946,Fundamental Theory, (Cambridge: Cambridge University Press).

    MATH  Google Scholar 

  • Ernst, F. J. 1968,Phys. Rev.,168, 1415–7.

    Article  ADS  Google Scholar 

  • Geroch, R., Held, A., Penrose, R. 1973, “A spacetime calculus based on pairs of null directions,J. Math. Phys.,14, 874–81.

    Article  MATH  Google Scholar 

  • Hawking, S. W. 1966, “The occurrence of singularities in cosmology”,Proc. R. Soc. (London),A294, 511.

    ADS  Google Scholar 

  • Hawking, S. W. 1972, “Black holes in general relativity”,Comm. Math. Phys.,25, 152.

    Article  ADS  Google Scholar 

  • Hawking, S. W., Ellis, G. F. R. 1973,The Large-Scale Structure of Space-Time, (Cambridge: Cambridge University Press).

    MATH  Google Scholar 

  • Hawking, S. W., Penrose, R. 1970, The singularities of gravitational collapse and cosmology,Proc. R. Soc. (London),A314, 529–548.

    ADS  Google Scholar 

  • Israel, W. 1967, “Event horizons in static vacuum spacetimes”,Phys. Rev.,164, 1776.

    Article  ADS  Google Scholar 

  • 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.

    Article  ADS  Google Scholar 

  • Kerr, R. P. 1963, “Gravitational field of a spinning mass as an example of algebraically special metrics”,Phys. Rev. Lett.,11, 237.

    Article  MATH  ADS  Google Scholar 

  • Khan, K. A., Penrose, R. 1971,Nature,229, 185.

    Article  ADS  Google Scholar 

  • 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).

    Google Scholar 

  • Lifshitz, E. M., Khalatnikov, I. M. 1963, “Investigations in relativistic cosmology”, inAdvances in Physics,12, 185.

    Article  ADS  Google Scholar 

  • Mason, L. J., Woodhouse, N. M. J. 1996,Integrability, Self-Duality, and Twistor Theory, (Oxford: Oxford University Press).

    MATH  Google Scholar 

  • McNamara, J. M. 1978a,Proc. R. Soc. London,A358, 499.

    ADS  Google Scholar 

  • McNamara, J. M. 1978b,Proc. R. Soc. London,A364, 121.

    ADS  Google Scholar 

  • 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.

    Article  Google Scholar 

  • 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).

    Google Scholar 

  • Nutku, Y., Halil, M. 1977,Phys. Rev. Lett.,39, 1379.

    Article  ADS  Google Scholar 

  • Oppenheimer, J. R., Snyder, H. 1939, “On continued gravitational contraction”,Phys. Rev.,56, 455–9.

    Article  MATH  ADS  Google Scholar 

  • Oppenheimer, J. R., Volkoff, H. 1939, “On massive neutron cores”,Phys. Rev.,55, 374.

    Article  MATH  ADS  Google Scholar 

  • Page, D. N. 1976, “Dirac equation around a charged, rotating black hole”,Phys. Rev. D.,14, 1509.

    Article  ADS  Google Scholar 

  • Penrose, R. 1965, “Gravitational collapse and spacetime singularities”,Phys. Rev. Lett.,14, 579.

    Article  ADS  Google Scholar 

  • Penrose, R. 1969, “Gravitational collapse: the role of general relativity,Rivista del Nuovo Cimento”,Numero speciale,1, 252–276.

    Google Scholar 

  • Penrose, R. 1973,Ann. N.Y. Acad. Sci.,224, 125.

    Article  ADS  Google Scholar 

  • 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).

    Google Scholar 

  • Penrose, R. 1979, “Singularities and Time-Asymmetry”, inGeneral Relativity, eds. S. W. Hawking & W. Israel (Cambridge: Cambridge University Press).

    Google Scholar 

  • Robinson, D. C. 1975,Phys. Rev. Lett.,34, 905.

    Article  ADS  Google Scholar 

  • Regge, T., Wheeler, J. A. W., 1957, “Stability of a Schwarzschild singularity”,Phys. Rev.,108, 1063.

    Article  MATH  ADS  Google Scholar 

  • Simpson, M., Penrose, R. 1973,Int. J. Theor. Phys.,7, 183.

    Article  Google Scholar 

  • Synge, J. L. 1950, “The gravitational field of a particle”,Proc. Irish Acad.,A53, 83.

    Google Scholar 

  • Teukolsky, S. A. 1973, “Perturbations of a rotating black hole: Fundamental equations for gravitational, electromagnetic, and neutrinofield perturbations”,Astrophys. J.,185, 635.

    Article  ADS  Google Scholar 

  • Walker, M., Penrose, R. 1970, “On quadratic first integrals of the geodesic equations for type 22 spacetimes”,Comm. Math. Phys.,18, 265.

    Article  MATH  ADS  Google Scholar 

  • Woodhouse, N. M. J., Mason, L. J. 1988, “The Geroch group and non-Hausdorff twistor spaces”,Nonlinearity,1, 73–114.

    Article  MATH  ADS  Google Scholar 

  • Zerilli, F. J. 1970,Phys. Rev. D.,2, 2141.

    Article  ADS  Google Scholar 

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Penrose, R. Chandrasekhar, black holes, and singularities. J Astrophys Astron 17, 213–231 (1996). https://doi.org/10.1007/BF02702305

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