Phase Structure of Higher Spin Black Hole

TL;DR

This paper explores the phase structures of higher spin black holes in AdS3, deriving a universal entropy formula and identifying multiple solution branches for spin 3, spin tilde 4, and G2 gravities, revealing complex thermodynamic behaviors.

Contribution

It introduces a universal entropy-charge relation for higher spin black holes and maps out their phase structures across different spin cases, extending previous results.

Findings

Six solution branches in spin 3 black holes.

Eight solution branches in spin tilde 4 black holes.

Twelve solution branches in G2 gravity.

Abstract

In this paper, we investigate the phase structures of the black holes with one single higher spin hair, focusing specifically on the spin 3 and spin tilde 4 black holes. Based on dimensional analysis and the requirement of having consistent thermodynamics, we derive an universal formula relating the entropy and the conserved charges for arbitrary AdS3 higher spin black holes. Then we use it to study the phase structure of the higher spin black holes. We find that there are six branches of solutions in the spin 3 gravity, eight branches of solutions in the spin tilde 4 gravity and twelve branches of solutions in the G2 gravity. In each case, all branches are related by a simple angle shift in the entropy functions. In the spin 3 case, we reproduce all the results found before. In the spin tilde 4 case, we find that in the low temperature it is at the BTZ branch while in the high temperature it transits to one of two other branches, depending on the signature of the chemical potential, a reflection of charge conjugate asymmetry found before.