Entropy Bounds for Rotating AdS Black Holes

TL;DR

This paper introduces new thermodynamic inequalities for rotating AdS black holes, incorporating thermodynamic volume, supported by analytical solutions, and suggesting broader applicability to non-spherical horizon topologies like black rings.

Contribution

It proposes novel inequalities involving thermodynamic volume for AdS black holes, extending the reverse isoperimetric inequality and testing their validity across various solutions.

Findings

Inequalities hold for a wide range of analytical black hole solutions.

Evidence suggests applicability to black holes with non-spherical horizons.

Valid for thin black rings in AdS.

Abstract

We propose novel thermodynamic inequalities that apply to stationary asymptotically Anti-de Sitter (AdS) black holes. These inequalities incorporate the thermodynamic volume and refine the reverse isoperimetric inequality. To assess the validity of our conjectures, we apply them to a wide range of analytical black hole solutions, observing compelling evidence in their favour. Intriguingly, our findings indicate that these inequalities may also apply for black holes of non-spherical horizon topology, as we show their validity as well for thin black rings in AdS.