Astrophysics and Space Science

, Volume 342, Issue 2, pp 329–332 | Cite as

Gravitational collapse without black holes

  • Trevor W. MarshallEmail author
Original Article


The contemporary notion of black hole originates in Oppenheimer and Snyder’s 1939 article “On Continued Gravitational Contraction” (Phys. Rev. 56:455, 1939). In particular, Penrose (Phys. Rev. Lett. 14:57, 1965) showed that their metric gave rise to trapped surfaces, that is regions of space from which no light rays can escape, and proved that within such surfaces black-hole formation is inevitable. Section “No trapped surfaces” of this article shows that a simple modification of the Oppenheimer-Snyder metric, fully consistent with General Relativity, may be made, so that all radial light rays originating in the interior escape to the exterior. There is no trapped surface and no black hole; on the contrary there is a stable end state with finite density, contained within a sphere of Schwarzschild radius. Implications for the interpretation of General Relativity, and also for experimental observation of supermassive objects and the Event Horizon Telescope project, are discussed in the concluding section.


Gravitational collapse Causality Gravitational field Trapped surface Oppenheimer-Snyder Event Horizon Telescope 



I wish to express my thanks to Dr Max Wallis for valuable discussion and suggestions.


  1. Babak, S.V., Grishchuk, L.P.: Phys. Rev. D 61, 024038 (1999) MathSciNetADSCrossRefGoogle Scholar
  2. Einstein, A.: Sitz.ber. Preuss. Akad. Wiss. Berl. Philos.-Hist. Kl. 1, 154–167 (1918) Google Scholar
  3. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge U. P., Cambridge (1973) zbMATHCrossRefGoogle Scholar
  4. Logunov, A.A.: Theory of Gravity. Nauka, Moscow (2001) Google Scholar
  5. Logunov, A.A., Mestvirishvili, M.A.: Theor. Math. Phys. 170(3), 413–419 (2012) MathSciNetCrossRefGoogle Scholar
  6. Marshall, T.W.: Gravitational waves versus black holes. arXiv:0707.0201 (2007)
  7. Marshall, T.W.: The gravitational collapse of a dust ball. arXiv:0907.2339 (2009)
  8. Marshall, T.W.: Fields tell matter how to move. arXiv:1103.6168 (2011)
  9. Marshall, T.W., Wallis, M.K.: J. Cosmol. 6, 1473–1484 (2010) ADSGoogle Scholar
  10. Mitra, A.: Astrophys. Space Sci. 332, 43–48 (2011) ADSCrossRefGoogle Scholar
  11. Oppenheimer, J.R., Snyder, H.: Phys. Rev. 56, 455 (1939) ADSzbMATHCrossRefGoogle Scholar
  12. Oppenheimer, J.R., Volkoff, G.: Phys. Rev. 54, 540 (1939) ADSCrossRefGoogle Scholar
  13. Penrose, R.: Phys. Rev. Lett. 14, 57 (1965) MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. Thorne, K.S.: Black Holes and Time Warps. Norton, New York (1994) zbMATHGoogle Scholar
  15. Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972) Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  1. 1.Buckingham Centre for AstrobiologyThe University of BuckinghamBuckinghamUK

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