The singularities of gravitational collapse and cosmology

@article{Hawking1970TheSO,
  title={The singularities of gravitational collapse and cosmology},
  author={Stephen William Hawking and Roger Penrose},
  journal={Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences},
  year={1970},
  volume={314},
  pages={529 - 548}
}
  • S. Hawking, R. Penrose
  • Published 27 January 1970
  • Mathematics
  • Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences
A new theorem on space-time singularities is presented which largely incorporates and generalizes the previously known results. The theorem implies that space-time singularities are to be expected if either the universe is spatially closed or there is an ‘object’ undergoing relativistic gravitational collapse (existence of a trapped surface) or there is a point p whose past null cone encounters sufficient matter that the divergence of the null rays through p changes sign somewhere to the past… 

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