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

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}=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.

12 pages 2 figures, Some references and 2 figures are added with minor changes. Final version for publication in European Physical Journal C

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• Spherically symmetric black holes in $f(R)$ gravity: Is geometric scalar hair supported ?
• Shadow of a Charged Rotating Black Hole in $f(R)$ Gravity
• Thermodynamic geometry of black holes in f(R) gravity
• Thermodynamic topology of black Holes in f(R) gravity
• Solar System tests and chameleon effect in f (R) gravity
• Rotating black strings in $f(R)$-Maxwell theory
• Static spherically symmetric Einstein-Yang-Mills-dilaton black hole and its thermodynamics
• Regular solutions in $f(T)$-Yang-Mills theory
• Static spherically symmetric black hole's solution in Einstein-Maxwell-Yang-Mills-dilaton theory
• Colliding plane wave solution in F(R)=R^{N} gravity
• Cosmic acceleration in asymptotically Ricci flat Universe