Penrose-Hawking singularity theorems

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In general relativity, there are several versions of the Penrose-Hawking singularity theorem. Most versions state, roughly, that if there is a trapped null surface and the energy density is nonnegative, then there exist geodesics of finite length which can't be extended.

References

The classic reference.

These theorems,strictly speaking,prove that there is at least one non-spacelike geodesic that is only finitely extendible into the past but there are cases in which the conditions of these theorems obtain in such a way that all past-directed spacetime paths terminate at a singularity. into the past.

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