CFT Phase Transition Analysis of Charged, Rotating Black Holes in $D=4$: A Holographic Thermodynamics Approach

TL;DR

This paper explores the complex phase transitions of charged, rotating black holes in four-dimensional AdS space using holographic thermodynamics, revealing new phenomena by varying multiple thermodynamic variables.

Contribution

It introduces a comprehensive analysis of phase transitions in Kerr-Newman AdS black holes across various ensembles, highlighting the effects of charge, angular momentum, and CFT pressure.

Findings

Identification of Van der Waals-type phase transitions.

Discovery of (de)confinement and Davies-type phase transitions.

Observation of novel critical behavior in specific ensembles.

Abstract

We investigate the holographic thermodynamics of 4-D Kerr-Newman AdS black holes, focusing on the conformal thermal states that are dual to these black holes. We explore the thermodynamic behavior within specific ensembles characterized by fixed sets of variables: $(\mathcal{Q},\mathcal{J},\mathcal{V},C)$, $(\mathcal{Q},\Omega,\mathcal{V},C)$, $(\varphi,\Omega,\mathcal{V},C)$, $(\varphi,\mathcal{J},\mathcal{V},C)$, $(\mathcal{Q},\Omega,p,C)$, and $(\varphi,\Omega,p,C)$. Here, $\varphi$, $\mathcal{Q}$, $\Omega$, $\mathcal{J}$, $p$, $\mathcal{V}$, and $C$ represent the electric potential, electric charge, angular velocity, angular momentum, CFT pressure, CFT volume, and central charge, respectively. The inclusion of both charge and momentum significantly enriches the regime of phase transitions, leading to a variety of phenomena including first-order Van der Waals-type phase transitions, (de)confinement phase transitions, Davies-type phase transitions, and second-order superfluid $\lambda$-type phase transitions. Notably, the introduction of the CFT pressure variable allows us to identify phase transitions and critical behavior in the $(\mathcal{Q},\Omega,p,C)$ and $(\varphi,\Omega,p,C)$ ensembles, which had not been previously observed. This study underscores the complexity and richness of phase transitions in these systems due to the inclusion of both charge and angular momentum.