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

TL;DR

The paper investigates global charges and thermodynamics of 3D higher spin black holes with relaxed AdS asymptotics using the canonical Regge-Teitelboim formalism within a Chern-Simons framework. Analyzing two explicit N=3 solutions (AGKP and CM), it shows that energy and other charges acquire nonlinear contributions from deviations from the background, necessitating integrability conditions that relate integration constants. For AGKP, the energy depends nonlinearly on constants, constrained by δ^2E=0 via a function F, while for CM holonomy fixes lead to E ∝ T^2 and a Cardy-consistent entropy with central charge c=3l/(2G). The results reinforce that relaxed asymptotics modify global charges yet remain compatible with holographic expectations and Cardy’s formula, highlighting subtle boundary-condition dependences in higher spin gravity.

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.