Clausius Equation for Horizons in $F(R)$ Gravity

TL;DR

This paper derives thermodynamic properties of horizons in $F(R)$ gravity using a covariant Hamiltonian approach, establishing an analogy with the Clausius equation and comparing results to classical General Relativity.

Contribution

It introduces a covariant Hamiltonian formulation for $F(R)$ gravity to derive horizon temperature and entropy, linking gravitational equations to thermodynamics.

Findings

Horizon temperature and entropy are derived in $F(R)$ gravity.

An analogy between Einstein equations and the Clausius equation is established.

Results are compared with classical General Relativity, highlighting differences and similarities.

Abstract

Covariant Hamiltonian formulation of $F(R)$ gravity is used to find variation of surface Hamiltonian which leads to formulation of temperature and entropy of a horizon. These thermodynamic quantities are then used to establish an analogy between Einstein equation and Clausius equation. The obtained results are compared to those from classical General Relativity.