f(R) Black holes

TL;DR

This paper explores modified gravity black holes with constant curvature, analyzing their thermodynamics and solutions, including Reissner-Nordström-AdS and Einstein-Yang-Mills black holes, using both analytical and numerical methods.

Contribution

It introduces new solutions for $f(R)$-Maxwell and $f(R)$-Yang-Mills black holes, connecting them to known Einstein solutions and providing asymptotic and numerical analyses.

Findings

Reissner-Nordström-AdS black hole recovered via $f(R)$ modifications.

Asymptotic solutions for $f(R)$-Yang-Mills black holes obtained.

Numerical confirmation of the existence of these black hole solutions.

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.