Testing the microstructure of $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes

TL;DR

This paper investigates the phase transition and microstructure of $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes using thermodynamic geometry, revealing universal small-large black hole transitions and microstructural interaction changes.

Contribution

It provides new insights into black hole microstructure and phase transitions in Gauss-Bonnet gravity, highlighting the role of horizon radius as an order parameter and microstructural interaction variations.

Findings

Small-large black hole phase transition is universal.

Horizon radius acts as an order parameter.

Microstructure interactions can be repulsive or change during phase transition.

Abstract

Understanding black hole microstructure via the thermodynamic geometry can provide us with more deeper insight into black hole thermodynamics in modified gravities. In this paper, we study the black hole phase transition and Ruppeiner geometry for the $d$-dimensional charged Gauss-Bonnet anti-de Sitter black holes. The results show that the small-large black hole phase transition is universal in this gravity. By reducing the thermodynamic quantities with the black hole charge, we clearly exhibit the phase diagrams in different parameter spaces. Of particular interest is that the radius of the black hole horizon can act as the order parameter to characterize the black hole phase transition. We also disclose that different from the five-dimensional neutral black holes, the charged ones allow the repulsive interaction among its microstructure for small black hole of higher temperature. Another significant difference between them is that the microscopic interaction changes during the small-large black hole phase transition for the charged case, where the black hole microstructure undergoes a sudden change. These results are helpful for peeking into the microstructure of charged black holes in the Gauss-Bonnet gravity.