The action for higher spin black holes in three dimensions

TL;DR

This paper computes the on-shell action for higher spin black holes in three dimensions within a Chern-Simons framework, demonstrating consistent thermodynamics and solving integrability conditions.

Contribution

It provides a detailed calculation of the on-shell action for spin N black holes, ensuring thermodynamic consistency in a Chern-Simons formulation.

Findings

On-shell action generates consistent thermodynamics.

Chern-Simons action satisfies integrability conditions.

Supports the validity of higher spin black hole thermodynamics.

Abstract

In the context of (2+1)--dimensional Chern-Simons SL(N,R)\times SL(N,R) gauge fields and spin N black holes we compute the on-shell action and show that it generates sensible and consistent thermodynamics. In particular, the Chern-Simons action solves the integrability conditions recently considered in the literature.