Some exact solutions of F(R) gravity with charged (a)dS black hole interpretation

Abstract

In this paper we obtain topological static solutions of some kind of pure $F(R)$ gravity. The present solutions are two kind: first type is uncharged solution which corresponds with the topological (a)dS Schwarzschild solution and second type has electric charge and is equivalent to the Einstein-$\Lambda$-conformally invariant Maxwell solution. In other word, starting from pure gravity leads to (charged) Einstein-$\Lambda$ solutions which we interpreted them as (charged) (a)dS black hole solutions of pure $F(R)$ gravity. Calculating the Ricci and Kreschmann scalars show that there is a curvature singularity at $r=0$. We should note that the Kreschmann scalar of charged solutions goes to infinity as $r \rightarrow 0$, but with a rate slower than that of uncharged solutions.