Quantum inequalities for quantum black holes

TL;DR

This paper develops spacetime inequalities for quantum-corrected black holes in three dimensions, extending previous proposals to all orders of backreaction and suggesting cosmic censorship persists non-perturbatively.

Contribution

It introduces refined quantum Penrose and reverse isoperimetric inequalities valid for all known 3D asymptotically AdS quantum black holes, beyond perturbative regimes.

Findings

Quantum Penrose inequality holds at all backreaction orders in 3D.

Quantum reverse isoperimetric inequality implies a maximum entropy state.

Previous inequalities fail beyond perturbation in three dimensions.

Abstract

We formulate spacetime inequalities applicable to quantum-corrected black holes to all orders of backreaction in semiclassical gravity. Namely, we propose refined versions of the quantum Penrose and reverse isoperimetric inequalities, valid for all known three-dimensional asymptotically anti-de Sitter quantum black holes. Previous proposals of the quantum Penrose inequality apply in higher dimensions but fail when applied in three dimensions beyond the perturbative regime. Our quantum Penrose inequality, valid in three dimensions, holds at all orders of backreaction. This suggests cosmic censorship must exist in non-perturbative semiclassical gravity. Our quantum reverse isoperimetric inequality implies a maximum entropy state for quantum black holes at fixed volume.