Thermodynamic Properties of Modified Black Hole Metrics in $f(R)$ Gravity

TL;DR

This paper derives modified Schwarzschild and Kerr-Newman black hole solutions within $f(R)$ gravity, exploring how alternative gravity theories affect black hole metrics and their thermodynamic properties.

Contribution

It introduces a method to construct new black hole metrics in $f(R)$ gravity, extending classical solutions with corrections from modified gravity theories.

Findings

Derived corrected black hole metrics in $f(R)$ gravity

Analyzed thermodynamic properties of these modified solutions

Provided a framework for exploring dark energy effects in black hole spacetimes

Abstract

To construct new Schwarzschild and Kerr-Newman metric solutions, we start from the Lagrangian in entropy and statistical mechanics, introducing $f(R)$ gravity theory and dark energy definitions. Through a series of calculations, we derive the corrected metric solutions under different forms of $f(R)$ gravity.