Thermodynamic geometry of black holes in f(R) gravity

TL;DR

This paper analyzes the thermodynamic behavior, stability, and phase transitions of various black holes in f(R) gravity using multiple thermodynamic geometry methods, highlighting parameter effects on stability and phase structure.

Contribution

It introduces a comprehensive thermodynamic geometric analysis of black holes in f(R) gravity, exploring stability and phase transitions with multiple methods and parameter dependencies.

Findings

Number and type of phase transitions depend on black hole parameters.

Curvature scalars from thermodynamic geometries correlate with phase transition points.

Parameter variations significantly influence black hole stability conditions.

Abstract

In this paper, we consider three types (static, static charged and rotating charged) of black holes in f(R) gravity. We study the thermodynamical behavior, stability conditions and phase transition of these black holes. It will be shown that, the number and type of phase transition points are related to different parameters, which shows the dependency of stability conditions to these parameters. Also, we extended our study to different thermodynamic geometry methods (Ruppeiner, Weinhold and GTD). Next, we investigate the compatibility of curvature scalar of geothermodynamic methods with phase transition points of the above balck holes. In addition, we point out the effect of different values of spacetime parameters on stability conditions of mentioned black holes.