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

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}=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 ω\rightarrow(1/3) (the ultra relativistic case in 4 - dimensions) and ω\rightarrow-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.

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