R\'enyi second laws for black holes

TL;DR

This paper extends the second law of black hole thermodynamics using Rényi entropies, revealing new constraints on black hole mergers in AdS space that are often more restrictive than the traditional area theorem.

Contribution

It introduces a Rényi entropy-based second law for black holes, providing novel restrictions on black hole mergers beyond the classical area increase theorem.

Findings

Rényi second laws impose additional constraints on black hole mergers.

In many cases, Rényi inequalities are more restrictive than the area theorem.

New bounds on the final states of black hole mergers in AdS space.

Abstract

Hawking's black hole area theorem provides a geometric realization of the second law of thermodynamics and constrains gravitational processes. In this work we explore a one-parameter extension of this constraint formulated in terms of the monotonicity properties of R\'enyi entropies. We focus on black hole mergers in asymptotically AdS space and determine new restrictions which these R\'enyi second laws impose on the final state. We evaluate the entropic inequalities starting from the thermodynamic ensembles description of black hole geometries, and find that for many situations they set more stringent bounds than those imposed by the area increase theorem.