Quantum singularities

Two spatial regions B and R are hyperentangled if the generalized entropy satisfies $S^{{B}\cup{R}}_{gen}$ < $S^R_{gen}$. If in addition all future (or all past) directed inward null shape deformations of B decrease $S^{{B}\cup{R}}_{gen}$, then we show that the causal development of B, with R hel...

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Bibliographic Details
Published in:Physical review. D 2023-03, Vol.107 (6), Article 066002
Main Authors: Bousso, Raphael, Shahbazi-Moghaddam, Arvin
Format: Article
Language:English
Subjects:
ASTRONOMY AND ASTROPHYSICS
entanglement in field theory
general relativity
quantum fields in curved spacetime
quantum gravity
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Summary:Two spatial regions B and R are hyperentangled if the generalized entropy satisfies $S^{{B}\cup{R}}_{gen}$ < $S^R_{gen}$. If in addition all future (or all past) directed inward null shape deformations of B decrease $S^{{B}\cup{R}}_{gen}$, 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.
ISSN:2470-0010
2470-0029
DOI:10.1103/PhysRevD.107.066002