Thermodynamics of black hole in $D$-dimensional $f(R)$ theory

TL;DR

This paper investigates the thermodynamic properties of black holes in higher-dimensional $f(R)$ gravity, deriving formulas for entropy and energy, and applying them to specific black hole solutions.

Contribution

It provides general formulas for entropy and energy of spherically symmetric black holes in $D$-dimensional $f(R)$ gravity and applies these to particular cases.

Findings

Derived formulas for entropy and energy in higher-dimensional $f(R)$ gravity.

Calculated thermodynamic quantities for specific black hole solutions.

Confirmed the applicability of the horizon-first law in these theories.

Abstract

We consider whether the new horizon-first law works in higher-dimensional $f(R)$ theory. We firstly obtain the general formulas to calculate the entropy and the energy of a general spherically-symmetric black hole in $D$-dimensional $f(R)$ theory. For applications, we compute the entropies and the energies of some black hokes in some interesting higher-dimensional $f(R)$ theories.