Thermodynamic stability of modified Schwarzschild-AdS black hole in rainbow gravity

TL;DR

This paper explores the thermodynamics and phase transitions of Schwarzschild-AdS black holes within rainbow gravity, revealing a new Hawking-Page-like transition influenced by energy-dependent metrics.

Contribution

It extends previous Schwarzschild black hole thermodynamics studies to Schwarzschild-AdS black holes in rainbow gravity, introducing modified temperature and phase transition analysis.

Findings

Existence of a new Hawking-Page-like phase transition

Stable small black hole tunnels into a large black hole

Standard Hawking-Page transition from flat space to black hole

Abstract

In this paper, we have extended the previous study of the thermodynamics and phase transition of the Schwarzschild black hole in the rainbow gravity to the Schwarzschild-AdS black hole where metric depends on the energy of a probe. Making use of the Heisenberg uncertainty principle and the modified dispersion relation, we have obtained the modified local Hawking temperature and thermodynamic quantities in an isothermal cavity. Moreover, we carry out the analysis of constant temperature slices of a black hole. As a result, we have shown that there also exists another Hawking-Page-like phase transition in which case a locally stable small black hole tunnels into a globally stable large black hole as well as the standard Hawking-Page phase transition from a hot flat space to a black hole.