# 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} }

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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