1109.3655 (S. Habib Mazharimousavi et al.)

Constant curvature f(R) gravity coupled with Yang-Mills field    [PDF]

S. Habib Mazharimousavi, M. Halilsoy, T. Tahamtan

We consider the particular class of $f(R)$ gravities coupled with Yang -
Mills (YM) field in which the Ricci scalar $=R_{0}=$ constant in all dimensions
$d\geq 4$. 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.

View original: http://arxiv.org/abs/1109.3655