Thermodynamics of the Schwarzschild-AdS black hole with a minimal length

TL;DR

This paper investigates the thermodynamics of Schwarzschild-AdS black holes with minimal length using mass-smeared models, revealing unique phase structures and stability properties influenced by quantum-inspired mass distributions.

Contribution

It introduces novel mass-smeared models with delta-function-based densities and analyzes their thermodynamic phase structures and stability, extending understanding of quantum effects in black hole thermodynamics.

Findings

Both models do not decay into pure thermal radiation due to minimal length.

The models exhibit unique phase structures with stable configurations.

Thermodynamic properties are similar across various delta-function-based mass-smeared forms.

Abstract

Using the mass-smeared scheme of black holes, we study the thermodynamics of black holes. Two interesting models are considered. One is the self-regular Schwarzschild-AdS black hole whose mass density is given by the analogue to probability densities of quantum hydrogen atoms. The other model is the same black hole but whose mass density is chosen to be a rational fractional function of radial coordinates. Both mass densities are in fact analytic expressions of the ${\delta}$-function. We analyze the phase structures of the two models by investigating the heat capacity at constant pressure and the Gibbs free energy in an isothermal-isobaric ensemble. Both models fail to decay into the pure thermal radiation even with the positive Gibbs free energy due to the existence of a minimal length. Furthermore, we extend our analysis to a general mass-smeared form that is also associated with the ${\delta}$-function, and indicate the similar thermodynamic properties for various possible mass-smeared forms based on the ${\delta}$-function.