Eur. Phys. J. C (2012) 72: 1958
https://doi.org/10.1140/epjc/s10052-012-1958-5

Regular Article - Theoretical Physics

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

Department of Physics, Eastern Mediterranean University, G. Magusa, North Cyprus, Mersin 10, Turkey

^* e-mail: habib.mazhari@emu.edu.tr

Received: 1 February 2012
Revised: 3 March 2012
Published online: 28 March 2012

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≥4. Even in this restricted class the spacetime has unlimited scopes determined by an equation of state of the form P _eff=ωρ. Depending on the distance from the origin (or horizon of a black hole) the state function ω(r) takes different values. It is observed that (the ultra relativistic case in 4 dimensions) and ω→−1 (the cosmological constant) are the limiting values of our state function ω(r) in a spacetime centered by a black hole. This suggests that having a constant ω throughout spacetime around a charged black hole in f(R) gravity with constant scalar curvature is a myth.