An Entropy Formula for Higher Spin Black Holes via Conical Singularities

TL;DR

This paper derives a simple entropy formula for higher spin black holes in 2+1 dimensions using conical singularities, confirming thermodynamic consistency and matching previous results.

Contribution

It introduces a conical singularity method to compute higher spin black hole entropy, providing a new, straightforward formula consistent with thermodynamics.

Findings

Derived a universal entropy formula for higher spin black holes.

Confirmed the formula satisfies the first law of thermodynamics.

Achieved agreement with previous integration-based results.

Abstract

We consider the entropy of higher spin black holes in 2+1 dimensions using the conical singularity approach. By introducing a conical singularity along a non contractible cycle and carefully evaluating its contribution to the Chern Simons action, we derive a simple expression for the entropy of a general stationary higher spin black hole. The resulting formula is shown to satisfy the first law of thermodynamics, and yields agreement with previous results based on integrating the first law.