Phases of higher spin black holes: Hawking-Page, transitions between black holes and a critical point

TL;DR

This paper explores the complex thermodynamic phase structure of higher spin black holes in three dimensions, revealing phase transitions, a critical point, and stability differences based on the spin number parity.

Contribution

It provides a detailed analysis of the phase diagram for $sl(N; ext{R})$ higher spin black holes, including explicit results for $N=4$ and extrapolations to general $N$, highlighting stability distinctions.

Findings

Discovery of Hawking-Page transitions to AdS$_3$ vacuum.

Identification of first order phase transitions among black holes.

Detection of a second order critical point.

Abstract

We study the thermodynamic phase diagram of three-dimensional $sl(N;\mathbb{R})$ higher spin black holes. By analyzing the semi-classical partition function we uncover a rich structure that includes Hawking-Page transitions to the AdS$_3$ vacuum, first order phase transitions among black hole states, and a second order critical point. Our analysis is explicit for $N=4$ but we extrapolate some of our conclusions to arbitrary $N$. In particular, we argue that even $N$ is stable in the ensemble under consideration but odd $N$ is not.