Stability of remnants of Bardeen regular black holes in presence of thermal fluctuations

TL;DR

This paper investigates the stability and characteristics of Bardeen black hole remnants influenced by thermal fluctuations, revealing their role in entropy increase and thermodynamic stability near the remnant size.

Contribution

It introduces a detailed thermodynamic analysis of Bardeen black hole remnants considering thermal fluctuations, highlighting their impact on stability and entropy.

Findings

Thermal fluctuations increase entropy and induce a maximum at the remnant radius.

Remnants exhibit stable thermodynamic properties due to quantum gravity effects.

The first law of thermodynamics holds near the remnant size.

Abstract

In this paper, we discuss remnants of the Bardeen regular black hole motivated by using the concept of thermal fluctuations. First, we derive the equilibrium values of various thermodynamic quantities like entropy, Hawking temperature, pressure, internal energy, Helmholtz free energy and Gibbs free energy in the non-extended phase space. We then discuss geometrothermodynamics (GTD) of Bardeen black hole to study its stability. Next, we estimate the size of black hole remnant in terms of some known parameters of the black hole solution. Motivated by the fact that estimation of size, characteristics and stability of remnants of black holes could further increase our understanding of binary collisions, information loss paradox and dark energy, the black hole remnant, which gives an idea about stable mass left over after evaporation of black hole, is seen to owe its presence due to thermal fluctuations. We see that the thermal fluctuations bring an overall increase in entropy curve. However, in presence of thermal fluctuations, a positive kink, which signifies a maximum increase in the value of entropy, occurs at a certain value of horizon, which is exactly equal to the remnant radius. We observe that the thermal fluctuations, which are characteristics of quantum gravity, lead to stable values of thermodynamic quantities near the remnant radius. In presence of thermal fluctuations, we then derive various corrected thermodynamic potentials and also discuss the validity of first law of black hole thermodynamics for Bardeen black hole.