The singularities of gravitational collapse and cosmology

@article{Hawking1970TheSO,
  title={The singularities of gravitational collapse and cosmology},
  author={S. Hawking and R. 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 1970
  • Physics
  • 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… Expand
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  • S. Hawking
  • Physics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1967
The questions about singularities that remain to be answered are discussed. It is shown, without any assumption about causality, that there are fully general solutions which evolve from aExpand
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  • S. Hawking
  • Physics
  • Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1966
It is shown that singularities of space-time are inevitable if the Einstein equations hold, if matter has normal properties and if the universe satisfies certain reasonable global conditions. TheExpand
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