An Entropy Formula for Higher Spin Black Holes via Conical Singularities

TL;DR

The paper develops a general entropy formula for stationary higher spin black holes in 2+1 dimensions by extending the conical singularity method to Chern-Simons gravity. By regularizing singular connections and evaluating the deficit-induced contribution to the CS action, the authors derive an explicit entropy expression that reproduces the BTZ results and satisfies the first law when holonomy is held fixed. They show the entropy formula aligns with results obtained by integrating the first law in hs$[\lambda]$ theories, and argue its applicability to general higher spin gauge groups containing SL(2,R). This work provides a gauge-invariant, locally geometric understanding of black hole entropy in higher spin gravity and clarifies the connection between holonomy regularity and thermodynamic consistency.

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.