A singularity theorem for evaporating black holes

TL;DR

This paper introduces a new singularity theorem for evaporating black holes based on the smeared null energy condition, extending classical results to semiclassical gravity and addressing quantum violations of energy conditions.

Contribution

It proposes the smeared null energy condition (SNEC) and proves a singularity theorem for evaporating black holes within semiclassical gravity.

Findings

Extends Penrose singularity theorem to semiclassical gravity.

Provides theoretical support for black hole evaporation models.

Highlights the importance of SNEC in quantum gravity contexts.

Abstract

The classical singularity theorems of General Relativity rely on energy conditions that are easily violated by quantum fields. Here, we provide motivation for an energy condition obeyed in semiclassical gravity: the smeared null energy condition (SNEC), a proposed bound on the weighted average of the null energy along a finite portion of a null geodesic. Using SNEC as an assumption we proceed to prove a singularity theorem. This theorem extends the Penrose singularity theorem to semiclassical gravity and has interesting applications to evaporating black holes.