Quantum Singularities

TL;DR

This paper proves a quantum singularity theorem based on a quantum Bousso bound, predicting singularities in black hole interiors even when classical spacetime appears nonsingular, thus extending classical singularity results.

Contribution

It introduces a quantum singularity theorem that replaces the Null Energy Condition with a quantum Bousso bound, predicting singularities in black hole interiors.

Findings

Quantum singularities obstruct semiclassical evolution.

The theorem predicts past singularities in black holes.

Classical spacetime remains nonsingular, but quantum effects cause singularities.

Abstract

Two spatial regions $B$ and $R$ are hyperentangled if the generalized entropy satisfies $S_{\text{gen}}^{B\cup R}<S_{\text{gen}}^R$. If in addition all future (or all past) directed inward null shape deformations of $B$ decrease $S_{\text{gen}}^{B\cup R}$, then we show that the causal development of $B$, with $R$ held fixed, must be incomplete. This result eliminates the Null Energy Condition from the assumptions of a recently proven singularity theorem. Instead, we assume a quantum version of the Bousso bound. Taking $R$ to contain the Hawking radiation after the Page time, our theorem predicts a singularity in the past causal development of the black hole interior. This is surprising because the classical spacetime is nonsingular in the past. However, one finds that Cauchy slices that are required to contain $R$ do not remain in the semiclassical regime. The quantum singularities predicted by our theorem are an obstruction to further semiclassical evolution, generalizing the singularities of classical general relativity.