Thermodynamic geometric analysis of BTZ black hole in f(R,{\phi}) Gravity

TL;DR

This paper explores the thermodynamic geometry of BTZ black holes within f(R) gravity, deriving exact models, calculating thermodynamic quantities, and analyzing phase transitions through Ruppeiner geometry compared to van der Waals systems.

Contribution

It provides the first detailed thermodynamic geometric analysis of BTZ black holes in f(R) gravity, including exact model derivation and phase transition insights.

Findings

Thermodynamic quantities like temperature and entropy are computed and compared.

Ruppeiner geometry reveals phase transition characteristics similar to van der Waals fluids.

Exact f(R) models for black hole solutions are obtained.

Abstract

In this work, we obtain the thermodynamic geometry of the extended black hole solution under f(R) gravity. This is the foundation of our work. We also obtain the exact form of the f(R) model for some solutions. In the thermodynamic analysis, we calculate the thermodynamic quantities such as temperature and entropy of these solutions and compare them with the corresponding BTZ black holes. After that, we study the Ruppeiner geometry, such as the f(R)-gravity (extended black hole solution) of the BTZ black hole, and analyze the thermodynamic comparison of the Ruppeiner geometry with the van der Waals equation for its phase transition process.