Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes

TL;DR

This paper explores the phase transition behavior of RN-AdS black holes, demonstrating universal critical exponents similar to van der Waals fluids, and uses thermodynamic geometry to analyze critical points.

Contribution

It provides a detailed analysis of critical phenomena and thermodynamic geometry of RN-AdS black holes, revealing universality in their phase transitions.

Findings

Critical exponents match those of van der Waals fluids.

Scalar curvature diverges at the critical point.

Thermodynamic geometry indicates phase transition points.

Abstract

The phase transition of Reissner-Nordstr\"om black holes in $(n+1)$-dimensional anti-de Sitter spacetime is studied in details using the thermodynamic analogy between a RN-AdS black hole and a van der Waals liquid gas system. We first investigate critical phenomena of the RN-AdS black hole. The critical exponents of relevant thermodynamical quantities are evaluated. We find identical exponents for a RN-AdS black hole and a Van der Waals liquid gas system. This suggests a possible universality in the phase transitions of these systems. We finally study the thermodynamic behavior using the equilibrium thermodynamic state space geometry and find that the scalar curvature diverges exactly at the van der Waals-like critical point where the heat capacity at constant charge of the black hole diverges.