Advertisement

Relativity pp 259-291 | Cite as

Singularities

  • Robert Geroch

Abstract

The goals of this paper are (1) to outline in general terms the present status of work on singularities, and (2) to discuss some of the outstanding problems in the subject and to indicate possible lines of attack on these problems. Our point of view will he an optimistic one: we shall concentrate more on what one would like to have than on what one is likely to get in the near future.

Keywords

Singular Point Minkowski Space Ideal Point Singular Solution Cauchy Surface 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Avez, A., Essais de Geometrie Riemannienne Hyperbolique Globale, Ann. Inst. Fourier, 13, 105 (1963).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bertotti, B., Uniform Electromagnetic Fields in the Theory of General Relativity, Phys. Rev., 116, 1331 (1959).MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Boyer, R.H., Lindquist, R.W., Maximal Analytic Extension of the Kerr Metric, J. Math. Phys., 8, 265 (1967).MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. 4.
    Choquet-Bruhat, Y., Geroch, R., Global Aspects of the Cauchy Problem in General Relativity, Comm. Math. Phys., (submitted for publication).Google Scholar
  5. 5.
    Clarke, C.J.S., On the Global Isometric Embedding of Pseudo-Riemannian Manifolds, (preprint, Carib. Univ., 1969 ).Google Scholar
  6. 6.
    Courant, R., Hilbert, D. Methods of Mathematical Physics II, ( Interscience, New York, 1965 ).Google Scholar
  7. 7.
    Ehresmann,C., Colloque de Topologie Algebrique (espaces fibres), Bruxelles, 1951.Google Scholar
  8. 8.
    Geroch, R., What is a Singularity in General Relativity?, Ann. Phys.,48, 526 (1968).Google Scholar
  9. 9.
    Geroch, R., Local Characterization of Singularities in General Relativity, J. Math. Phys., 9, 450 (1968).MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. 10.
    Geroch, R., The Structure of Singularities, article in Battelle Recontres, C. DeWitt, J. Wheeler, ed., ( Benjamin, New York, 1968 ).Google Scholar
  11. 11.
    Geroch, R., The Domain of Dependence, J. Math. Phvs., (to be published).Google Scholar
  12. 12.
    Geroch, R., Limits of Spacetimes, Comm. Math. Phvs., (to be published).Google Scholar
  13. 13.
    Geroch, R., Kronheimer, E.H., Penrose, R., Ideal Points in Spacetime, Proc. Roy. Soc., (submitted for publication).Google Scholar
  14. 14.
    Graves, J.C., Brill, D.R., Oscillatory Character of the Reissner-Nordström Metric for an Ideal Charged Wormhole, Phys. Rev., 120, 1507 (1960).MathSciNetADSzbMATHCrossRefGoogle Scholar
  15. 15.
    Hawking, S.W., The Occurrence of Singularities in Cosmology I, Proc. Roy. Soc., 291A, 511 (1966).MathSciNetADSCrossRefGoogle Scholar
  16. 16.
    Hawking, S.W., The Occurrence of Singularities in Cosmology II, Proc. Roy. Soc., 295A, 490 (1966).MathSciNetADSCrossRefGoogle Scholar
  17. 17.
    Hawking, S.W. The Occurrence of Singularities in Cosmology III, Proc. Rov. Soc., 300A, 187 (1967).ADSGoogle Scholar
  18. 18.
    Hawking, S.W., The Existence of Cosmic Time Functions, Proc. Roy. Soc., 308A, 433 (1969).Google Scholar
  19. 19.
    Hawking, S.W., Penrose, R., The Singularities of Gravitational Collapse and Cosmology, Proc. Roy. Soc., (submitted for publication).Google Scholar
  20. 20.
    Jordan, P., Ehlers, J., Kundt, W., Strenge Lösungen der Feldgleichungen der Allgemeinen Relativitätstheorie, Akad. Wiss. der Lit. Mainz (1960).Google Scholar
  21. 21.
    Kelly, J.L., General Topology, ( Van Nostrand, New York, 1955 )Google Scholar
  22. 22.
    Kruskal, M.D., Maximal Extension of the Schwarzschild Metric, Phys. Rev., 119, 1743 (1960).MathSciNetADSzbMATHCrossRefGoogle Scholar
  23. 23.
    Kundt, W., Note on the Completeness of Spacetimes, Zeit. für Physik, 172, 488 (1963).MathSciNetADSzbMATHCrossRefGoogle Scholar
  24. 24.
    Maitra, S.C., A Stationary Dust-Filled Cosmological Solution with Λ = 0 and Without Closed Timelike Lines, (preprint, Univ. of Maryland, 1965 ).Google Scholar
  25. 25.
    Melvin, M.A., Pure Magnetic and Electric Geons, Phys. Lett., 8, 65 (1964).Google Scholar
  26. 26.
    Misner, C.W., The Flatter Regions of Newman Unti and Tamburino’s Generalized Schwarzschild Space, J.. Math. Phys., 4, 924 (1963).Google Scholar
  27. 27.
    Misner, C.W., The Mix-Master Universe, (preprint, Univ. of Maryland, 1969 ).Google Scholar
  28. 28.
    Newman, E.T., Tamburino, L., Unti, T., Empty Space Generalization of the Schwarzschild Metric, J. Math. Phys., 4, 915 (1963).Google Scholar
  29. 29.
    Nowacki, V.W., Die Euklidischen, dreidimensionalen geschlossenen und offenen Raumformen, Comm. Math. Helv., 7, 81 (1934).MathSciNetCrossRefGoogle Scholar
  30. 30.
    Penrose, R., Gravitational Collapse and Space-Time Singularities, Phys. Rev. Lett.,14, 57 (1965).MathSciNetADSzbMATHCrossRefGoogle Scholar
  31. 31.
    Penrose, R., Zero Rest Mass Fields Including Gravitation, Asymptotic Behaviour, Proc. Roy. Soc., 284A, 159 (1965).MathSciNetADSGoogle Scholar
  32. 32.
    Penrose, R., Structure of Space-Time, article in Battelle Recontres, C. DeWitt, J. Wheeler, ed., ( Benjamin, New York, 1968.Google Scholar
  33. 33.
    Raychaudhuri, A., Relativistic Cosmology, Phys. Rev., 98, 1123 (1955).MathSciNetADSzbMATHCrossRefGoogle Scholar
  34. 34.
    Robinson, I., A Solution of the Maxwell-Einstein Equations, Bull. Acad. Polon. Sci., 7, 351 (1959).zbMATHGoogle Scholar
  35. 35.
    Shepley, L., S0(3,R) Homogeneous Cosmologies, (PhD thesis, Dept of Phys., Princeton, 1965 ).Google Scholar
  36. 36.
    Spanier, E.H., Algebraic Topolomv, (McGraw Hill, New York, 1966).Google Scholar
  37. 37.
    Synge, J.L. Relativity: The General Theory ( North-Holland, Amsterdam, 1960 ).zbMATHGoogle Scholar
  38. 38.
    Taub, A.H., Empty Spacetimes Admitting a Three-Parameter Group of Motions, Ann. Math., 53, 472 (1951).MathSciNetADSzbMATHCrossRefGoogle Scholar
  39. 39.
    Thorne, K.S., Gravitational Collapse, a Review-Tutorial Article (1968, to be published).Google Scholar

Copyright information

© Plenum Press, New York 1970

Authors and Affiliations

  • Robert Geroch
    • 1
  1. 1.Department of MathematicsBirkbeck CollegeLondonEngland

Personalised recommendations