Area Functional Relation for 5D-Gauss-Bonnet-AdS Black Hole

TL;DR

This paper derives area and entropy relations for 5D Gauss-Bonnet-AdS black holes, revealing mass-independent properties and exploring thermodynamic stability, phase transitions, and universal quantities related to black hole entropy.

Contribution

It introduces explicit area functional relations for multi-horizon 5D Gauss-Bonnet-AdS black holes, highlighting mass-independent features and their potential universality.

Findings

Some horizon area functions are mass-independent.

Entropy product relations are not mass-independent.

Phase transition conditions are identified.

Abstract

We present \emph{area (or entropy) functional relation} for multi-horizons five dimensional (5D) Einstein-Maxwell-Gauss-Bonnet-AdS Black Hole. It has been observed by exact and explicit calculation that some complicated function of two or three horizons area is \emph{mass-independent} whereas the entropy product relation is \emph{not} mass-independent. We also study the local thermodynamic stability of this black hole. The phase transition occurs at certain condition. \emph{Smarr mass formula} and \emph{first law} of thermodynamics have been derived. This \emph{mass-independent} relation suggests they could turn out to be an \emph{universal} quantity and further helps us to understanding the nature of black hole entropy (both interior and exterior) at the microscopic level. In the \emph{Appendix}, we have derived the thermodynamic products for 5D Einstein-Maxwell-Gauss-Bonnet black hole with \emph{vanishing} cosmological constant.