Area(or Entropy) Product Formula for a Regular Black Hole

TL;DR

This paper investigates the thermodynamic properties of a regular black hole, revealing that the entropy product depends on mass, but a related function remains mass-independent, and analyzes stability and phase transitions.

Contribution

It provides an exact calculation of the entropy product for a regular black hole and identifies a mass-independent quantity involving horizon areas, enhancing understanding of black hole thermodynamics.

Findings

Entropy product depends on mass parameter.

A mass-independent function of horizon areas exists.

Black hole exhibits second order phase transition under certain conditions.

Abstract

We compute the area(or entropy) product formula for a regular black hole derived by Ay\'on-Beato and Garc\'ia in 1998\cite{abg}. By explicit and exact calculation, it is shown that the entropy product formula of two physical horizons strictly \emph{depends} upon the ADM mass parameter that means it is \emph{not} an universal(mass-independent) quantity. But a slightly more complicated function of event horizon area and Cauchy horizon area is indeed a \emph{mass-independent} quantity. We also compute other thermodynamic properties of the said black hole. We further study the stability of such black hole by computing the specific heat for both the horizons. It has been observed that under certain condition the black hole possesses second order phase transition. The pictorial diagram of the phase transition is given.