Thermodynamic approach to field equations in Lovelock gravity and f(R) gravity revisited

TL;DR

This paper revisits the thermodynamic derivation of field equations in Lovelock and f(R) gravity, emphasizing the role of inner horizons in black hole thermodynamics for charged black holes.

Contribution

It provides a detailed analysis of the thermodynamic properties of black holes in Lovelock and f(R) gravity, highlighting the importance of inner horizons in the first law.

Findings

Inner horizons contribute significantly to black hole thermodynamics.

The first law can be derived considering both outer and inner horizons.

Revisiting these theories clarifies the thermodynamic structure of charged black holes.

Abstract

The first law of thermodynamics at black hole horizons is known to be obtainable from the gravitational field equations. A recent study claims that the contributions at inner horizons should be considered in order to give the conventional first law of black hole thermodynamics. Following this method, we revisit the thermodynamic aspects of field equations in the Lovelock gravity and f(R) gravity by focusing on two typical classes of charged black holes in the two theories.