A Brief Thermodynamic Study For Four Dimensional Einstein Gauss Bonnet Black Holes Using Fractalised Barrow Entropy

Abstract

Higher dimensional Gauss-Bonnet gravity can be particularized to a four dimensional case either using the Glavan, D. and Lin, C. type \cite{glavan2020einstein} limiting method or by the Hordenski type \cite{gurses2007gauss} metric compactification procedure. Depending on ADM mass and Gauss Bonnet coupling parameter $\alpha_{GB}$, a black hole solution is prescribed \cite{hennigar2020taking}. The phrase which is responsible for divergence at some finite values of radial coordinate stays inside a square root and thus softens the divergence. A quantum gravity affected surface formula for the black hole is chosen. Fractalized entropy thus formed is known as the Barrow Entropy\cite{ladghami2024barrow}. Global nature for such an entropy formula is discovered. Temperature is calculated with and without different quantum corrections. Stability with such temperature structures are analyzed. To support this, sign changes in specific heat, occurrences of double points in free energy, sign changes and jumps in derivatives of free energy etc are thoroughly discussed. Probable rise of phase transitions are pointed.