Constant curvature f(R) gravity minimally coupled with Yang-Mills field

TL;DR

This paper investigates constant scalar curvature f(R) gravity coupled with Yang-Mills fields, revealing that the effective equation of state parameter varies with distance, challenging the notion of a constant  around black holes.

Contribution

It introduces a class of f(R) gravity models with constant Ricci scalar coupled to Yang-Mills fields and analyzes the spatial variation of the effective equation of state parameter.

Findings

 approaches 1/3 near the black hole horizon

 approaches -1 at large distances

The equation of state parameter is not constant throughout spacetime.

Abstract

We consider the particular class of f(R) gravities minimally coupled with Yang - Mills (YM) field in which the Ricci scalar =R_{0}= constant in all dimensions d\geq4. Even in this restricted class the spacetime has unlimited scopes determined by an equation of state of the form P_{eff}={\omega}{\rho}. Depending on the distance from the origin (or horizon of a black hole) the state function {\omega}(r) takes different values. It is observed that {\omega}\rightarrow(1/3) (the ultra relativistic case in 4 - dimensions) and {\omega}\rightarrow-1 (the cosmological constant) are the limiting values of our state function {\omega}(r) in a spacetime centered by a black hole. This suggests that having a constant {\omega} throughout spacetime around a charged black hole in f(R) gravity with constant scalar curvature is a myth.