F(R) gravity equation of state

TL;DR

This paper derives the field equations of ${f f}(R)$ gravity as an equation of state within local space-time thermodynamics, extending Jacobson's arguments using a generalized entropy concept and an effective Newton constant.

Contribution

It introduces a novel derivation of ${f f}(R)$ gravity equations from thermodynamic principles, incorporating Wald's entropy and an effective Newton constant.

Findings

${f f}(R)$ gravity equations are obtained from thermodynamic considerations.

The derivation extends Jacobson's approach with a generalized entropy.

Uses an effective Newton constant for graviton exchange.

Abstract

The ${\bf f}(R)$ gravity field equations are derived as an equation of state of local space-time thermodynamics. Jacobson's arguments are non-trivially extended, by means of a more general definition of local entropy, for which Wald's definition of dynamic black hole entropy is used, as well as the concept of an effective Newton constant for graviton exchange, recently appeared in the literature.