Gravitational singularity

Summary

A gravitational singularity is a place where a spacetime of general relativity breaks down. Freely falling observers or light rays reach it in finite time and cannot be continued. Since the singular "points" are not part of the spacetime, the standard definition uses incomplete geodesics of a spacetime that cannot be extended. Examples are the centre $r = 0$ of the Schwarzschild metric and the big bang of cosmological models. The Penrose–Hawking singularity theorems show that singularities form under general physical conditions.