Ruppeiner geometry and the fluctuation of the RN-AdS black hole in framework of the extensive thermodynamics

TL;DR

This paper explores the Ruppeiner geometry and thermodynamic fluctuations of four-dimensional RN-AdS black holes within an extensive thermodynamics framework, revealing how the central charge influences fluctuation probabilities.

Contribution

It introduces a novel analysis of RN-AdS black hole thermodynamics using extensive variables and the central charge, extending the understanding of black hole phase transitions and fluctuations.

Findings

Increasing central charge reduces fluctuation probability.

The thermodynamic framework applies across different gravitational models.

Phase transition behavior is reexamined using density variables.

Abstract

The Ruppeiner geometry and the fluctuation for a four-dimensional charged AdS black hole in the framework of the extensive thermodynamics have been investigated. By fixing the AdS radius of Vissers construction, the extensive thermodynamics of the RN-AdS black hole is established, and the central charge plays the role of particle number. With the thermodynamic variables density, we reexamine the phase transition of the black hole, and the result will hold for the black holes under different gravitational models. Moreover, we have studied the Ruppeiner geometry and the black hole fluctuation, and show that the increase of central charge will reduce the fluctuation probability.