Phase Structure of Kerr-AdS Black Hole

TL;DR

This paper investigates the phase transitions and critical phenomena of Kerr-AdS black holes, revealing phase structures, stability conditions, and critical exponents matching mean field theory.

Contribution

It provides a detailed analysis of the phase structure and critical behavior of Kerr-AdS black holes, including stability criteria and scaling symmetry, which advances understanding of black hole thermodynamics.

Findings

Identified multiple phase transition temperatures ($T_{L}$, $T_{c1}$, $T_{c2}$).

Calculated critical exponents matching mean field theory ($eta=1/2$, $ u=1/2$, etc.).

Mapped phase diagram and discussed free energy scaling symmetry.

Abstract

We study the critical phenomena of Kerr-AdS black hole. Phase structures are observed at different temperatures, $T_{L}$, $T_{c1}$ and $T_{c2}$ with various features. We discuss the thermal stability considering the isothermal compressibility and how phase transitions related to each other. The asymptotic value of the angular momentum also has an implication on separating stable and unstable part. Near critical temperature $T_{c1}$, the order parameter is determined to calculate the critical exponents. All the critical exponents ($\alpha$,$\beta$,$\gamma$,$\delta$)=(0,1/2,1,3) are identical to that of mean field systems. We plot the phase diagram near this critical point, and discuss the scaling symmetry of the free energy.