Analytical and exact critical phenomena of $d$-dimensional singly spinning Kerr-AdS black holes

TL;DR

This paper analytically and numerically investigates the critical phenomena of $d$-dimensional singly spinning Kerr-AdS black holes, revealing unique critical points, phase diagrams, and reentrant phase transitions across different dimensions.

Contribution

It provides the first analytical critical point for $d=4$ and exact numerical critical points for $d=5$ to $9$, including reentrant phase transition points, without approximations.

Findings

Analytical critical point for $d=4$.

Numerical critical points for $d=5$ to $9$.

Existence of two critical points for $d extgreater=6$, with only the larger participating in phase transitions.

Abstract

In the extended phase space, the $d$-dimensional singly spinning Kerr-AdS black holes exhibit the van der Waals's phase transition and reentrant phase transition. Since the black hole system is a single characteristic parameter thermodynamic system, we show that the form of the critical point can be uniquely determined by the dimensional analysis. When $d=4$, we get the analytical critical point. The coexistence curve and phase diagrams are obtained. The result shows that the fitting form of the coexistence curve in the reduced parameter space is independent of the angular momentum. When $d=5$---$9$, the exact critical points are numerically solved. It demonstrates that when $d\geq6$, there are two critical points. However, the small one does not participate in the phase transition. Moreover, the exact critical reentrant phase transition points are also obtained. All the critical points are obtained without any approximation.