Gravitational R\'enyi entropy from corner terms

TL;DR

This paper introduces a novel method to compute gravitational Rnyi entropy using corner terms, avoiding regularization and applicable to higher-curvature gravity theories, based on first principles and corner term variations.

Contribution

It presents a consistent, first principles approach to calculate gravitational Rnyi entropy via Hayward corner terms, extending to higher-curvature theories without regularization.

Findings

Corner term equals entropy functional for fixed-area states.

Method does not require regularization of conical singularities.

Approach extends naturally to higher-curvature gravity theories.

Abstract

We provide a consistent first principles prescription to compute gravitational R\'enyi entropy using Hayward corner terms. For Euclidean solutions to Einstein gravity, we compute R\'enyi entropy of Hartle--Hawking and fixed--area states by cutting open a manifold containing a conical singularity into a wedge with a corner. The entropy functional for fixed--area states is equal to the corner term itself, having a flat-entanglement spectrum, while extremization of the functional follows from the variation of the corner term under diffeomorphisms. Notably, our method does not require regularization of the conical singularity, and naturally extends to higher-curvature theories of gravity.