Hawking Radiation and $P-v$ Criticality of Charged Dynamical (Vaidya) Black Hole in Anti-de Sitter Space

TL;DR

This paper explores the thermodynamic behavior and phase transitions of charged dynamical Vaidya black holes in Anti-de Sitter space, revealing modifications in critical parameters due to dynamical effects.

Contribution

It introduces a detailed analysis of Hawking radiation and $P-v$ criticality for dynamical charged AdS black holes, extending static black hole thermodynamics to dynamical scenarios.

Findings

Critical pressure, volume, and temperature relationships are modified by black hole dynamics.

Critical exponents remain unchanged despite the dynamical nature.

P-v criticality disappears when the horizon change rate exceeds a critical value.

Abstract

We study Hawking radiation and $P-v$ criticality of charged dynamical (Vaidya) black hole in Anti-de Sitter (AdS) space. By investigating the near horizon properties of scalar field, we derive Hawking temperature of dynamical charged (Vaidya) AdS black hole. Based on this result, by regarding the cosmological constant as the thermodynamic pressure, we investigate the analogy between the charged dynamical (Vaidya) AdS black holes in the ensemble with the fixed charge and van der Waals liquid-gas system in detail, including equation of state, $P-v$ diagram, critical point, heat capacities and critical exponents near the critical point. It is shown that the relationship among the critical pressure, critical volume, and critical temperature gets modified while the critical exponents are not affected by the dynamical nature of the black hole. We also find that, when the rate of change of the black hole horizon exceeds the critical value, the $P-v$ criticality of the charged dynamical (Vaidya) AdS black hole will disappear.