Thermodynamic geometric analysis of BTZ black hole under f(R) gravity

TL;DR

This paper explores the thermodynamics and phase transitions of BTZ black holes within f(R) gravity, deriving exact solutions and analyzing their thermodynamic geometry in anti-de Sitter space.

Contribution

It provides new exact BTZ black hole solutions in dilaton f(R)-gravity and analyzes their thermodynamic phase structure and Ruppeiner geometry.

Findings

Derived exact BTZ solutions in f(R)-gravity.

Analyzed thermodynamic quantities and phase transitions.

Studied the Ruppeiner geometry of the black holes.

Abstract

In this work, we obtained the black hole solutions in the expansion f(R)-gravitation (R is not regarded as a constant here), and studied their thermodynamics, especially the phase transition and criticality in anti-de Sitter Behavior (AdS) expands the phase space. We obtained accurate Banados, Teitelboim and Zanelli (BTZ) corresponding solutions in dilaton f(R)-gravity, which is the basis of our work. We also obtained the exact form of the f(R) model for some solutions. In thermodynamic analysis, we calculate thermodynamic quantities such as temperature and entropy of these solutions and compare them with the corresponding quantities of BTZ. After that, we study the Ruppeiner geometry, such as the f(R)-gravity of the BTZ black hole, and analyze its phase transition process Ruppeiner geometry.