Phase transition and microstructures of five-dimensional charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble

TL;DR

This paper investigates the phase transition and microstructure interactions of five-dimensional charged Gauss-Bonnet-AdS black holes in the grand canonical ensemble, revealing microstructural changes and interaction types during phase transitions.

Contribution

It constructs the coexistence curve analytically, analyzes microstructure interactions via Ruppeiner geometry, and uncovers constant interaction properties at phase transitions in this black hole system.

Findings

Identified a sudden change in microstructures during phase transition.

Found that low electric potential leads to attractive interactions, high potential leads to repulsive.

Discovered the normalized scalar curvature has a critical exponent of 2 and a universal constant -1/8.

Abstract

In this paper, we study the small-large black hole phase transition and construct the Ruppeiner geometry for the five-dimensional charged Gauss-Bonnet-AdS black hole in the grand canonical ensemble. By making use of the equal area law, we obtain the analytical coexistence curve of the small and large black holes. Then the phase diagrams are examined. We also calculate the change of the thermodynamic volume during the small-large phase transition, which indicates that there exists a sudden change among the black hole microstructures. The corresponding normalized scalar curvature of the Ruppeiner geometry is also calculated. Combing with the empirical observation of scalar curvature, we find that for low electric potential, the attractive interaction dominates among the microstructures, while a high electric potential produces repulsive interactions. In the reduced parameter space, we observe that only attractive interaction is allowed when the coexistence region is excluded. The normalized scalar curvature also admits a critical exponent 2 and a universal constant $-\frac{1}{8}$. In particular, the value of the normalized scalar curvature keeps the same along the coexistence small and large black hole curves. So in the grand canonical ensemble, the interaction can keep constant at the phase transition where the black hole microstructures change. These results disclose the intriguing microstructures for the charged AdS black hole in the Gauss-Bonnet gravity.