Black hole solutions in f(R) gravity coupled with non-linear Yang-Mills field

TL;DR

This paper explores black hole solutions in f(R) gravity coupled with a non-linear Yang-Mills field across various dimensions, providing both numerical and exact solutions, including a specific 6D case with f(R)=√R.

Contribution

It demonstrates the existence of black hole solutions in higher-dimensional f(R) gravity coupled with non-linear Yang-Mills fields, including an exact solution in six dimensions.

Findings

Black hole solutions with single or double horizons are found.

f(R) can be determined numerically for general cases.

An exact f(R)=√R solution is obtained in 6 dimensions.

Abstract

It is shown that in the static, spherically symmetric spacetime the problem of metric f(R) gravity coupled with non-linear Yang-Mills (YM) field constructed from the Wu-Yang ansatz as source, can be solved in all dimensions. By non-linearity 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)=\surdR gravity that couples with the YM field in a consistent manner.