# Repulsive Interactions and Universal Properties of Charged Anti-de Sitter Black Hole Microstructures

## TL;DR

This paper uses Ruppeiner geometry to analyze charged AdS black hole microstructures, revealing unique repulsive interactions at high temperature and small sizes, distinct from Van der Waals fluids, and identifying universal properties.

## Contribution

It uncovers the presence of repulsive microstructure interactions in small, high-temperature black holes and identifies universal properties of these interactions.

## Key findings

- Repulsive interactions dominate for small, high-temperature black holes.
- Repulsive interaction strength is independent of charge and temperature.
- The Ruppeiner curvature near criticality matches that of Van der Waals fluids.

## Abstract

The Ruppeiner geometry of thermodynamic fluctuations provides a powerful diagnostic of black hole microstructures. We investigate this for charged AdS black holes and find that while an attractive microstructure interaction dominates for most parameter ranges, a weak repulsive interaction dominates for small black holes of high temperature. This unique property distinguishes the black hole system from that of a Van der Waals fluid, where only attractive microstructure interactions are found. We also find two other novel universal properties for charged black holes. One is that the repulsive interaction is independent of the black hole charge and temperature. The other is that the behavior of the Ruppeiner curvature scalar near criticality is characterized by a dimensionless constant that is identical to that for a Van der Waals fluid, providing us with new insight into black hole microstructures.