# The occurrence of singularities in cosmology

@article{Hawking1966TheOO, title={The occurrence of singularities in cosmology}, author={Stephen William Hawking}, journal={Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences}, year={1966}, volume={294}, pages={511 - 521} }

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. The singularities would be in the past and would, in principle, be observable. Observation to determine whether such singularities actually occurred would provide a powerful test of the Einstein equations in strong fields. The singularity would not necessarily constitute a beginning of the universe.

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## References

SHOWING 1-2 OF 2 REFERENCES

### Geometry of Manifolds

- Mathematics
- 1964

Manifolds Lie groups Fibre bundles Differential forms Connexions Affine connexions Riemannian manifolds Geodesics and complete Riemannian manifolds Riemannian curvature Immersions and the second…

### geometry of manifolds. A cadem ic P ress. C arte r

- B . 1966 Phys. Rev
- 1964