Communications in Mathematical Physics

, Volume 99, Issue 4, pp 613–625 | Cite as

The effect of spherical shells of matter on the Schwarzschild black hole

  • Tevian Dray
  • Gerard 't Hooft
Article

Abstract

Based on previous work we show how to join two Schwarzschild solutions, possibly with different masses, along null cylinders each representing a spherical shell of infalling or outgoing massless matter. One of the Schwarzschild masses can be zero, i.e. one region can be flat. The above procedure can be repeated to produce space-times with aC0 metric describing several different (possibly flat) Schwarzschild regions separated by shells of matter. An exhaustive treatment of the ways of combining four such regions is given; the extension to many regions is then straightforward. Cases of special interest are: (1) the scattering of two spherical gravitational “shock waves” at the horizon of a Schwarzschild black hole, and (2) a configuration involving onlyone external universe, which may be relevant to quantization problems in general relativity. In the latter example, only an infinitesimal amount of matter is sufficient to remove the “Wheeler wormhole” to another universe.

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References

  1. 1.
    Dray, T., 't Hooft, G.: The gravitational shock wave of a massless particle. Nucl. Phys. B253, 173 (1985)Google Scholar
  2. 2.
    't Hooft, G.: On the quantum structure of a black hole. Utrecht preprint, 1984Google Scholar
  3. 3.
    Synge, J.L.: A model in general relativity for the instantaneous transformation of a massive particle into radiation. Proc. Roy. Irish Acad.59, 1 (1957)Google Scholar
  4. 4.
    Penrose, R.: In: General relativity: Papers in honour of J.L. Synge, p. 101. Ó Raifeartaigh, L. ed. Oxford: Clarendon Press 1972Google Scholar
  5. 5.
    D'Eath, P.D.: High-speed black-hole encounters and gravitational radiation. Phys. Rev. D18, 990 (1978); Curtis, G.E.: Twistors and linearized Einstein theory on plane-fronted impulsive wave backgrounds, and Ultrarelativistic black-hole encounters. J. Gen. Rel. Grav.9, 987 and 999 (1978)Google Scholar
  6. 6.
    Kahn, K.A., Penrose, R.: Scattering of two impulsive gravitational plane waves. Nature229, 185 (1971)Google Scholar
  7. 6a.
    Szekeres, P.: Colliding gravitational waves. Nature228, 1183 (1970)Google Scholar
  8. 6b.
    Szekeres, P.: Colliding plane gravitational waves. J. Math. Phys.13, 286 (1972)Google Scholar
  9. 6c.
    Nutku, Y., Halil, M.: Colliding impulsive gravitational waves. Phys. Rev. Lett.39, 1379 (1977)Google Scholar
  10. 6d.
    Chandrasekhar, S., Xanthopoulos, B.C.: On colliding waves in the Einstein-Maxwell theory. University of Chicago preprint, 1984Google Scholar
  11. 7.
    't Hooft, G.: Ambiguity of the equivalence principle and Hawking's temperature. J. Geom. Phys.1, 45 (1984)Google Scholar
  12. 8.
    Taub, A.: Space-times with distribution-valued curvature tensors. J. Math. Phys.21, 1423 (1980)Google Scholar
  13. 9.
    Vaidya, P.C.: The gravitational field of a radiating star. Proc. Ind. Acad. Sci. A33, 264 (1951)Google Scholar
  14. 10.
    Hiscock, W.A.: Models of evaporating black holes. I, and -II. Effects of the outgoing created radiation. Phys. Rev. D23, 2813 and 2823 (1981)Google Scholar
  15. 11.
    Hiscock, W.A., Williams, L.G., Eardley, D.M.: Creation of particles by shell-focusing singularities. Phys. Rev. D26, 751 (1982)Google Scholar

Copyright information

© Springer-Verlag 1985

Authors and Affiliations

  • Tevian Dray
    • 1
    • 2
  • Gerard 't Hooft
    • 2
  1. 1.School of MathematicsInstitute for Advanced StudyPrincetonUSA
  2. 2.Instituut voor Theoretische FysicaUtrechtThe Netherlands

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