The Return of the Singularities: Applications of the Smeared Null Energy Condition

TL;DR

This paper introduces the smeared null energy condition (SNEC) as a physically motivated energy condition in semiclassical gravity, proves a related singularity theorem, and explores its implications for black holes and wormholes.

Contribution

It formulates the SNEC, proves a semiclassical singularity theorem based on it, and applies the results to black hole evaporation and traversable wormholes.

Findings

Proved a semiclassical singularity theorem using SNEC.

Applied SNEC to analyze evaporating black holes.

Discussed implications for traversable wormholes.

Abstract

The classic singularity theorems of General Relativity rely on energy conditions that can be violated in semiclassical gravity. Here, we provide motivation for an energy condition obeyed by 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. We then prove a semiclassical singularity theorem using SNEC as an assumption. This theorem extends the Penrose theorem to semiclassical gravity. We also apply our bound to evaporating black holes and the traversable wormhole of Maldacena-Milekhin-Popov, and comment on the relationship of our results to other proposed semiclassical singularity theorems.