Vacuum energy and the latent heat of AdS-Kerr black holes

TL;DR

This paper explores phase transitions of rotating AdS black holes, analyzing how fixed angular momentum versus fixed angular velocity affect the nature of these transitions, including critical points and latent heat behavior.

Contribution

It provides a detailed comparison of phase transition behaviors under fixed angular momentum and fixed angular velocity, including analytic phase boundary forms and latent heat calculations.

Findings

Constant angular momentum leads to a second order phase transition with vanishing latent heat.

Constant angular velocity results in a phase transition with infinite latent heat at the critical point.

Analytic expressions for phase boundaries and Clapeyron equation verification are provided.

Abstract

Phase transitions for rotating asymptotically anti-de Sitter black holes in four dimensions are described in the $P-T$ plane, in terms of the Hawking temperature and the pressure provided by the cosmological constant. The difference between constant angular momentum and constant angular velocity is highlighted, the former has a second order phase transition while the latter does not. If the angular momentum is fixed there a line of first order phase transitions terminating at a critical point with a second order phase transition and vanishing latent heat, while if the angular velocity is fixed there is a line of first order phase transitions terminating at a critical point with infinite latent heat. For constant angular velocity the analytic form of the phase boundary is determined, latent heats derived and the Clapeyron equation verified.