Charged 4D Einstein-Gauss-Bonnet Black Hole: Vacuum solutions, Cauchy Horizon, Thermodynamics

TL;DR

This paper explores the thermodynamics and horizon structure of four-dimensional Einstein-Gauss-Bonnet black holes, revealing how the Cauchy horizon influences thermodynamic properties and confirming the area law with logarithmic corrections.

Contribution

It introduces a new parameterization for black hole thermodynamics, analyzes the effects of the Cauchy horizon, and provides a physical interpretation of the logarithmic entropy correction.

Findings

Thermodynamic variables are expressed in a new parameterization.

The Cauchy horizon affects thermodynamic parameters.

Entropy obeys the area law with a logarithmic correction.

Abstract

In this paper, we investigate the four-dimensional Einstein-Gauss-Bonnet black hole. The thermodynamic variables and equations of state of black holes are obtained in terms of a new parameterization. We discuss a formulation of the van der Waals equation by studying the effects of the temperature on P-V isotherms. We show the influence of the Cauchy horizon on the thermodynamic parameters. We prove by different methods, that the black hole entropy obey area law (plus logarithmic term that depends on the Gauss-Bonnet coupling {\alpha}). We propose a physical meaning for the logarithmic correction to the area law. This work can be extended to the extremal EGB black hole, in that case, we study the relationship between compressibility factor, specific heat and the coupling {\alpha}.