The European Physical Journal H

, Volume 39, Issue 4, pp 403–411 | Cite as

Stephen Hawking’s 1966 Adams Prize Essay

  • George F.R. Ellis
Regular article


Quantum Gravity Gravitational Collapse Gravitational Radiation Null Geodesic Cosmological Solution 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Bondi, H. 1960. Cosmology (Cambridge University Press).Google Scholar
  2. 2.
    Carter, B. 1971. Causal structure in space-time. Gen. Rel. Grav. 1: 349-391.ADSCrossRefzbMATHGoogle Scholar
  3. 3.
    Cohn, P.M. 1957. Lie groups (Cambridge Tracts in Mathematics and Mathematical Physics, No. 46.) (Cambridge University Press, New York).Google Scholar
  4. 4.
    Dodelson, S. 2003. Modern Cosmology (Academic Press).Google Scholar
  5. 5.
    Ehlers, J. 1961. Contributions to the Relativistic Mechanics of Continuous Media. Akademie der Wissenschaften und Literatur (Mainz), Abhandlungen der Mathematisch-Naturwissenschaftlichen Klasse Nr. 11, pp. 792-837. Reprinted Gen. Rel. Grav. 25: 1225-66 (1993). Google Scholar
  6. 6.
    Einstein, A. 1915. Die Feldgleichungen der Gravitation. Sitzungsber. Preuss. Akad. Wiss. Berlin (Math. Phys.) 1915: 844-847. zbMATHGoogle Scholar
  7. 7.
    Ellis, G.F.R. 1971. Relativistic Cosmology. Proceedings of the International School of Physics “Enrico Fermi”, Course 47: General relativity and cosmology, edited by R.K. Sachs (Academic Press), pp. 104-182. Reprinted: Gen. Rel. Grav. 41: 581 (2009).Google Scholar
  8. 8.
    Ellis, G.F.R. and B.G. Schmidt. 1977. Singular space-times. Gen. Rel. Grav. 11: 915-953.ADSCrossRefMathSciNetGoogle Scholar
  9. 9.
    Ellis, G.F.R. and R. Maartens. 2004. The Emergent Universe: inflationary cosmology with no singularity. Class. Quant. Grav. 21: 223-232.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  10. 10.
    Ellis, G.F.R., R. Maartens and M.A.H. MacCallum. 2012. Relativistic Cosmology (Cambridge University Press). Google Scholar
  11. 11.
    Geroch, R. 1966. Singularities in closed universes. Phys. Rev. Lett. 17: 445-447.ADSCrossRefzbMATHGoogle Scholar
  12. 12.
    Geroch, R. 1968. Local Characterization of Singularities in General Relativity. J. Math. Phys. 9: 450.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    Geroch, R. 1970. Domain of Dependence. J. Math. Phys. 11: 437.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Gödel, K. 1949. An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation. Rev. Mod. Phys. 21: 447. Reprinted: Gen. Rel. Grav. 32: 1409 (2000).ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    Gödel, K. 1952. Rotating Universes in General Relativity Theory. Proceedings of the International Congress of Mathematicians, edited by L.M. Graves et al., Cambridge, Mass. Vol. 1, p. 175. Reprinted Gen. Rel. Grav. 32: 1419 (2000).Google Scholar
  16. 16.
    GRG Bulletin on General Relativity and Gravitation. 1965. Report on the London Conference on general relativity and gravitation. September 1965, Vol. 9, Issue 1, pp. 1-2Google Scholar
  17. 17.
    Guth, A.H. 1981. Inflationary universe: A possible solution to the horizon and flatness problems. Phys. Rev. D 23: 347-356.ADSCrossRefGoogle Scholar
  18. 18.
    Hawking, S.W. 1965a. Occurrence of singularities in open universes. Phys. Rev. Lett. 15: 689-690.ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    Hawking, S.W. 1965b. Singularities and the geometry of space-time. Ph.D. Thesis, Cambridge.Google Scholar
  20. 20.
    Hawking, S.W. 1966a. Singularities in the universe. Phys. Rev. Lett. 17: 444-445.ADSCrossRefGoogle Scholar
  21. 21.
    Hawking, S.W. 1966b. The Occurrence of singularities in cosmology. Proc. Roy. Soc. Lond. A294: 511-521. ADSCrossRefMathSciNetGoogle Scholar
  22. 22.
    Hawking, S.W. 1966c. Perturbations of an expanding universe. ApJ 145: 544-554. ADSCrossRefGoogle Scholar
  23. 23.
    Hawking, S.W. 1966d. The Occurrence of singularities in cosmology. II. Proc. Roy. Soc. Lond. A295: 490-49. ADSCrossRefMathSciNetGoogle Scholar
  24. 24.
    Hawking, S.W. 1966e. Singularities and the Geometry of Spacetime. Adams Prize Essay (unpublished).Google Scholar
  25. 25.
    Hawking, S.W. 1967. The occurrence of singularities in cosmology. III. Causality and singularities. Proc. Roy. Soc. Lond. A300: 187-201. ADSCrossRefGoogle Scholar
  26. 26.
    Hawking, S.W. 1968. The Existence of cosmic time functions. Proc. Roy. Soc. Lond. A308: 433-435. ADSGoogle Scholar
  27. 27.
    Hawking, S.W. 1970. The conservation of matter in general relativity. Commun. Math. Phys. 18: 301-306.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  28. 28.
    Hawking, S.W. 1971. Stable and generic properties in general relativity. Gen. Rel. Grav. 1: 393-400.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  29. 29.
    Hawking, S.W. 2014. Singularities and the Geometry of Spacetime. Eur. Phys. J. H, DOI:  10.1140/epjh/e2014-50013-6
  30. 30.
    Hawking, S.W. and G.F.R. Ellis. 1965. Singularities in homogeneous world models. Phys. Lett. 17: 246-247.ADSCrossRefMathSciNetGoogle Scholar
  31. 31.
    Hawking, S.W. and G.F.R. Ellis. 1968. The Cosmic black body radiation and the existence of singularities in our universe. ApJ 152: 25.ADSCrossRefGoogle Scholar
  32. 32.
    Hawking, S.W. and G.F.R. Ellis. 1973. The Large scale structure of space-time (Cambridge University Press, Cambridge). Google Scholar
  33. 33.
    Hawking, S.W. and R. Penrose. 1970. The Singularities of gravitational collapse and cosmology. Proc. Roy. Soc. Lond. A314: 529-548. ADSCrossRefMathSciNetGoogle Scholar
  34. 34.
    Heckmann, O. and E. Schücking. 1962. Relativistic Cosmology. In Gravitation, an Introduction to Current Research, edited by L. Witten, Wiley, New York, p. 438.Google Scholar
  35. 35.
    Helgason, S. 1962. Differential geometry and symmetric spaces (Academic Press).Google Scholar
  36. 36.
    Jordan, P., J. Ehlers and R. Sachs. 1961. Exact solutions of the field equations of general relativity. II. Contributions to the theory of pure gravitational radiations. Akad. Wiss. Lit. Mainz Abhandl. Mat. Nat. Kl. Klasse Nr 1: 1-62. Reprinted in English: Gen. Rel. Grav. 45: 2691-753 (2013).Google Scholar
  37. 37.
    Kristian, J. and R.K. Sachs. 1966. Observations in cosmology. ApJ 143: 379.ADSCrossRefMathSciNetGoogle Scholar
  38. 38.
    Kronheimer, E.H. and R. Penrose. 1967. The structure of causal spaces. Mathematical Proceedings of the Cambridge Philosophical Society 63: 481-501.CrossRefzbMATHMathSciNetGoogle Scholar
  39. 39.
    Kruskal, M.D. 1960. Maximal extension of Schwarzschild metric. Phys. Rev. 119: 1743-1745. ADSCrossRefzbMATHMathSciNetGoogle Scholar
  40. 40.
    Kundt, W. 1968. Recent Progres in Cosmology. Springer Tracts modern physics 47: 111-142.ADSCrossRefGoogle Scholar
  41. 41.
    Kundt, W. and M. Trümper. 1962. Beiträge zur Theorie der Stahlungsfelder. Akad. Wiss. Lit. in Mainz, Abh. Math.-nat. Klasse, Nr. 12. Google Scholar
  42. 42.
    Maartens, R. and B.A. Bassett. 1998. Gravito-electromagnetism. Class. Quantum Grav. 15: 705.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  43. 43.
    Milnor, J.W. 1963. Morse theory (Princeton University Press).Google Scholar
  44. 44.
    Newman, E.T. and R. Penrose. 1962. An Approach to Gravitational Radiation by a Method of Spin Coefficients. J. Math. Phys. 3: 566.ADSCrossRefMathSciNetGoogle Scholar
  45. 45.
    Oppenheimer, J.R. and H. Snyder. 1939. On Continued Gravitational Contraction. Phys. Rev. 56: 455-459.ADSCrossRefzbMATHGoogle Scholar
  46. 46.
    Penrose, R. 1963. Conformal treatment of infinity. In Relativity, Groups, and Topology, edited by C. de Witt and B. de Witt (Gordon and Breach). Reprinted Gen. Rel. Grav. 43: 901-22 (2011).Google Scholar
  47. 47.
    Penrose, R. 1965. Gravitational collapse and space-time singularities. Phys. Rev. Lett. 14: 57.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  48. 48.
    Penrose, R. 1972. Techniques in Differential Topology in Relativity. CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM).Google Scholar
  49. 49.
    Pirani, F.A.E. 1956. On the Physical Significance of the Riemann Tensor. Acta Physica Polonica 15: 389-405 (1956). Reprinted Gen. Rel. Grav. 41: 1216 (2009).ADSMathSciNetGoogle Scholar
  50. 50.
    Pirani, F.A.E. 1957. Invariant Formulation of Gravitational Radiation Theory. Phys. Rev. 105: 1089.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  51. 51.
    Raychaudhuri, A. 1955. Relativistic Cosmology. I. Phys. Rev. 98: 1123. Reprinted Gen. Rel. Grav. 32: 749 (2000).ADSCrossRefzbMATHMathSciNetGoogle Scholar
  52. 52.
    Rindler, W. 1956. Visual Horizons in World Models. Mon. Not. Roy. Astr. Soc. 116: 662-677. Reprinted: Gen. Rel. Grav. 34: 133 (2002).ADSCrossRefMathSciNetGoogle Scholar
  53. 53.
    Schmidt, B.G. 1971. A new definition of singular points in general relativity. Gen. Rel. Grav. 1: 269-280.ADSCrossRefzbMATHGoogle Scholar
  54. 54.
    Synge, J.L. 1934. On the Deviation of Geodesics and Null Geodesics, Particularly in Relation to the Properties of Spaces of Constant Curvature and Indefinite Line-Element. Ann. Math. 35: 705-713. Reprinted Gen. Rel. Grav. 41: 1206 (2009). CrossRefMathSciNetGoogle Scholar
  55. 55.
    Taub, A.H. 1951. Empty Space-Times Admitting a Three Parameter Group of Motions. Annals of Mathematics 53: 472-490. Reprinted: Gen. Rel. Grav. 36: 2699 (2004). ADSCrossRefzbMATHMathSciNetGoogle Scholar
  56. 56.
    Tipler, F.J. 1977. Singularities and causality violation. Annals of Physics 108: 1-36.ADSCrossRefzbMATHMathSciNetGoogle Scholar
  57. 57.
    Tipler, F.J. 1978. Energy conditions and spacetime singularities. Phys. Rev. D 17: 2521-2528. ADSCrossRefMathSciNetGoogle Scholar
  58. 58.
    Tipler, F.J., C.J.S. Clarke and G.F.R. Ellis. 1980. Singularities and Horizons. In General Relativity and Gravitation. One hundred years after the birth of Albert Einstein, edited by A. Held, Plenum Press, New York, Vol. 2, p. 97.Google Scholar
  59. 59.
    Wheeler, J.A. 1963. Geometrodynamics and the issue of the final state. In Relativity, Groups and Topology, edited by C. de Witt and B. de Witt, Gordon and Breach, New York, pp. 317-522.Google Scholar
  60. 60.
    Wheeler, J.A. 1996. At Home in the Universe (Masters of Modern Physics) (American Institute of Physics). Google Scholar
  61. 61.
    Zeeman, E.C. 1964. Causality implies the Lorentz group. J. Math. Phys. 5, 490.ADSCrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© EDP Sciences and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Mathematics Department, University of Cape TownRondeboschSouth Africa

Personalised recommendations