  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.

General Relativity and Quantum Cosmology