Black hole solutions inf(R)gravity coupled with nonlinear Yang-Mills field

Abstract

It is shown that in the static, spherically symmetric spacetime, the problem of metric $f(R)$ gravity coupled with nonlinear Yang-Mills (YM) field constructed from the Wu-Yang ansatz as source can be solved in all dimensions. By nonlinearity it is meant that the YM Lagrangian depends arbitrarily on its invariant. A particular form is considered to be in the power-law form with limit of the standard YM theory. The formalism admits black hole solutions with single or double horizons in which $f(R)$ can be obtained, in general numerically. In 6-dimensional case we obtain an exact solution given by $f(R)=\sqrt{R}$ gravity that couples with the YM field in a consistent manner.