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

TL;DR

This paper derives exact static solutions in pure F(R) gravity, including uncharged and charged (a)dS black holes, revealing how these solutions relate to Einstein-Maxwell solutions and analyzing their curvature singularities.

Contribution

It presents new exact static solutions in pure F(R) gravity that correspond to (a)dS black holes with and without charge, linking them to Einstein-Maxwell solutions.

Findings

Uncharged solutions match topological (a)dS Schwarzschild solutions.

Charged solutions are equivalent to Einstein-$\Lambda$-conformally invariant Maxwell solutions.

Curvature singularities exist at r=0, with charged solutions' singularity growth rate slower than uncharged ones.

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.