Multicritical Phase Transitions in Multiply Rotating Black Holes

TL;DR

This paper demonstrates the existence of multi-critical points with more than three phases in multiply rotating Kerr-AdS black holes across various dimensions, revealing that such complex phase structures are more common than previously believed.

Contribution

It explicitly identifies quadruple and quintuple points in higher-dimensional rotating black holes and provides a method to find multi-critical points with multiple phases.

Findings

Existence of quadruple points in 8D black holes

Existence of quintuple points in 10D black holes

Multi-critical points are more prevalent in black hole thermodynamics

Abstract

We show that multi-critical points in which more than three phases coalesce are present in multiply rotating Kerr-AdS black holes in $d$-dimensions. We explicitly present a quadruple point for a triply rotating black hole in $d=8$ and a quintuple point for a quadruply rotating black hole in $d=10$. The maximal number of distinct phases $n$ is one larger than the maximal number of independent rotations, and we outline a method for obtaining the associated $n$-tuple point. Situations also exist where more than three phases merge at sub-maximal multi-critical points. Our results show that multi-critical points in black hole thermodynamics are more common than previously thought, with systems potentially supporting many phases as long as a sufficient number of thermodynamic variables are present.