# Microstructure and continuous phase transition of RN-AdS black hole

## TL;DR

This paper investigates the microstructure and continuous phase transition of RN-AdS black holes, introducing a new order parameter and analyzing critical phenomena and molecular models to understand their microstructure differences.

## Contribution

It introduces a new order parameter and applies Landau theory to analyze the critical behavior and microstructure of RN-AdS black holes.

## Key findings

- Identifies different microstructures for charged and uncharged black hole molecules.
- Finds the critical exponent for the phase transition.
- Models black hole molecules as fermion and boson gases.

## Abstract

As is well known that RN-AdS black hole has a phase transition which is similar to that of van der Waals system. The phase transition depends on the electric potential of the black hole and is not the one between a large black hole and a small black hole. On this basis, we introduce a new order parameter and use the Landau continuous phase transition theory to discuss the critical phenomenon of RN-AdS black hole and give the critical exponent. By constructing the binary fluid model of black hole molecules, we investigate the microstructure of black holes. Furthermore, by studying the effect of the spacetime scalar curvature on the phase transition, we find that the charged and uncharged molecules of black holes are with different microstructure red which is like fermion gas and boson gas.