Thermodynamics of accelerating and supersymmetric $AdS_4$ black holes

TL;DR

This paper investigates the thermodynamics of accelerating, rotating, charged $AdS_4$ black holes, especially those with spindle horizons, using holography to derive their entropy and thermodynamic laws, including supersymmetric solutions.

Contribution

It introduces a comprehensive analysis of $AdS_4$ black holes with spindle horizons, extending thermodynamic understanding to supersymmetric and non-extremal cases via holography.

Findings

Derived a first law of thermodynamics for these black holes.

Obtained a simple expression for the on-shell action on the supersymmetric locus.

Calculated the Bekenstein-Hawking entropy for supersymmetric and extremal solutions.

Abstract

We study the thermodynamics of $AdS_4$ black hole solutions of Einstein-Maxwell theory that are accelerating, rotating, and carry electric and magnetic charges. We focus on the class for which the black hole horizon is a spindle and can be uplifted on regular Sasaki-Einstein spaces to give solutions of $D=11$ supergravity that are free from conical singularities. We use holography to calculate the Euclidean on-shell action and to define a set of conserved charges which give rise to a first law. We identify a complex locus of supersymmetric and non-extremal solutions, defined through an analytic continuation of the parameters, upon which we obtain a simple expression for the on-shell action. A Legendre transform of this action combined with a reality constraint then leads to the Bekenstein-Hawking entropy for the class of supersymmetric and extremal black holes.