A gravitational collapse singularity theorem consistent with black hole evaporation

TL;DR

This paper demonstrates that the traditional causality assumptions in gravitational collapse theorems can be relaxed, allowing for singularity formation consistent with black hole evaporation and quantum effects.

Contribution

It introduces a modified singularity theorem that does not rely on global hyperbolicity, aligning classical singularity results with quantum black hole evaporation.

Findings

Singularities can form without global hyperbolicity.

The causality conditions in Penrose's theorem can be largely removed.

Compatibility of singularity theorems with quantum black hole evaporation.

Abstract

The global hyperbolicity assumption present in gravitational collapse singularity theorems is in tension with the quantum mechanical phenomenon of black hole evaporation. In this work I show that the causality conditions in Penrose's theorem can be almost completely removed. As a result, it is possible to infer the formation of spacetime singularities even in the absence of predictability and hence compatibly with quantum field theory and black hole evaporation.