# Entropy and Energy of Static Spherically Symmetric Black Hole in $f(R)$ theory

## TL;DR

This paper derives formulas for entropy and energy of static spherically symmetric black holes in $f(R)$ gravity and applies them to specific solutions, advancing understanding of black hole thermodynamics in modified gravity.

## Contribution

It introduces a general framework for calculating black hole entropy and energy in $f(R)$ theories and applies it to various solutions, which was not previously done.

## Key findings

- Derived general formulas for black hole entropy and energy in $f(R)$ gravity.
- Calculated entropy and energy for specific black hole solutions in $f(R)$ models.
- Enhanced understanding of thermodynamics in modified gravity theories.

## Abstract

We consider the new horizon first law in $f(R)$ theory with general spherically symmetric black hole. We derive the general formulas to computed the entropy and energy of the black hole. For applications, some nontrivial black hole solutions in some popular $f(R)$ theories are investigated, the entropies and the energies of black holes in these models are first calculated.