Perturbed thermodynamics and thermodynamic geometry of a static black hole in $f (R)$ gravity

TL;DR

This paper explores the thermodynamic properties and geometric structure of a static black hole in $f(R)$ gravity, analyzing entropy corrections, phase transitions, and the impact of small fluctuations on thermodynamic geometry.

Contribution

It introduces a detailed study of thermodynamic geometry and entropy corrections for a static black hole in $f(R)$ gravity, highlighting the correlation between curvature scalar singularities and phase transitions.

Findings

Curvature scalar singularities coincide with heat capacity zeros.

Correction parameter influences thermodynamic behavior and phase transition points.

Geometrothermodynamics effectively detects phase transitions in the black hole.

Abstract

In this paper, we consider a static black hole in $f(R)$ gravity. We recapitulate the expression for corrected thermodynamic entropy of this black hole due to small fluctuations around equilibrium. Also, we study the geometrothermodynamics (GTD) of this black hole and investigate the adaptability of the curvature scalar of geothermodynamic methods with phase transition points of this black hole. Moreover, we study the effect of correction parameter on thermodynamic behaviour of this black hole. We observe that the singular point of the curvature scalar of Ruppeiner metric coincides completely with zero point of the heat capacity and the deviation occurs with increasing correction parameter.