Higher spin gravity in 3D: black holes, global charges and thermodynamics

TL;DR

This paper revisits the properties of 3D higher spin black holes, analyzing their global charges and thermodynamics, revealing nonlinear contributions and confirming the entropy matches the Cardy formula.

Contribution

It provides a detailed canonical analysis of higher spin black holes with relaxed asymptotics, highlighting nonlinear charge contributions and thermodynamic consistency.

Findings

Global charges include nonlinear deviations from background

First law of thermodynamics holds without work terms for some solutions

Black hole entropy matches the Cardy formula exactly

Abstract

Global charges and thermodynamic properties of three-dimensional higher spin black holes that have been recently found in the literature are revisited. Since these solutions possess a relaxed asymptotically AdS behavior, following the canonical approach, it is shown that the global charges, and in particular the mass, acquire explicit nontrivial contributions given by nonlinear terms in the deviations with respect to the reference background. It is also found that there are cases for which the first law of thermodynamics is fulfilled in the canonical ensemble, i.e., without work terms associated to the presence of higher spin fields, and remarkably, the semiclassical higher spin black hole entropy is exactly reproduced from Cardy formula.