Thermodynamics of charged AdS black holes in rainbow gravity

TL;DR

This paper investigates the thermodynamics of charged AdS black holes within rainbow gravity, revealing phase transition behaviors and stability conditions influenced by modified dispersion relations and the Heisenberg Uncertainty Principle.

Contribution

It introduces a novel analysis of black hole thermodynamics in rainbow gravity, including deformed temperature, heat capacity, and phase transition characteristics.

Findings

Identification of a critical behavior similar to liquid-gas systems.

Discovery of a special test particle mass causing zero temperature and diverging heat capacity.

Observation of characteristic swallow tail behavior in Gibbs function indicating phase transitions.

Abstract

In this paper, the thermodynamic property of charged AdS black holes is studied in rainbow gravity. By the Heisenberg Uncertainty Principle and the modified dispersion relation, we obtain deformed temperature. Moreover, in rainbow gravity we calculate the heat capacity in a fixed charge and discuss the thermal stability. We also obtain a similar behaviour with the liquid-gas system in extending phase space (including \(P\) and \(r\)) and study its critical behavior with the pressure given by the cosmological constant and with a fixed black hole charge \(Q\). Furthermore, we study the Gibbs function and find its characteristic swallow tail behavior, which indicates the phase transition. We also find there is a special value about the mass of test particle which would lead the black hole to zero temperature and a diverging heat capacity with a fixed charge.