f(R) Black holes

Abstract

We study the $f(R)$-Maxwell black hole imposed by constant curvature and its all thermodynamic quantities, which may lead to the Reissner-Nordstr\"om-AdS black hole by redefining Newtonian constant and charge. Further, we obtain the $f(R)$-Yang-Mills black hole imposed by constant curvature, which is related to the Einstein-Yang-Mills black hole in AdS space. Since there is no analytic black hole solution in the presence of Yang-Mills field, we obtain asymptotic solutions. Then, we confirm the presence of these solutions in a numerical way.