Critical phenomenon of quantum BTZ black holes

TL;DR

This paper investigates the phase transitions and critical phenomena of quantum BTZ black holes by analyzing their thermodynamic behavior, revealing novel features such as a critical point, unusual critical exponents, and stability conditions.

Contribution

It introduces treating the quantum backreaction parameter as a thermodynamic variable and explores the resulting phase structure and critical behavior, which differ from classical mean field predictions.

Findings

Critical point at ν_c=1 identified.

First order phase transitions depend on temperature relative to ν_c.

Critical exponents deviate from mean field theory and violate scaling laws.

Abstract

We extend the thermodynamics of quantum BTZ black holes by treating the quantum backreaction strength parameter $\nu$ as a thermodynamic variable. We find various novel features. The critical point appears at $\nu_c=1$ and a first order transition occurs either below the critical temperature for $\nu<\nu_c$ or above the critical temperature for $\nu>\nu_c$. By solving the coexistence curve analytically, we analyze the phase structures and clarify an unexpected discontinuity around the critical point. The critical exponents are significantly different from the mean field theory results and violate one of the scaling laws. We present an intepretation for this by using a universal three scale factor hypothesis for critical behavior of thermodynamic potential. Finally, we prove that given an arbitrarily small angular momenta, only one stable black hole phase can exist and hence no transition will occur.