A Quantum Singularity Theorem for the Evaporating Black Hole

TL;DR

This paper proves a new singularity theorem for evaporating black holes in semiclassical gravity, showing they are inherently incomplete without assuming traditional energy conditions.

Contribution

It introduces a singularity theorem that relies on weaker causality conditions and the Generalized Second Law, expanding understanding of black hole singularities.

Findings

Evaporating black holes are proven to be null geodesically incomplete.

The theorem does not require global hyperbolicity or null energy conditions.

It relies on weaker causality assumptions and the Generalized Second Law.

Abstract

We prove a singularity theorem in semiclassical gravity without assuming global hyperbolicity or the null energy/curvature condition; the former is replaced by the weaker causality conditions of stable causality and past reflectivity, and the latter is replaced as is standard by the Generalized Second Law. This establishes in particular that the standard models of evaporating black holes are singular - i.e. they are null geodesically incomplete.