Topological Static Spherically Symmetric vacuum Solutions in $\mathcal F(R,G)$ Gravity

TL;DR

This paper derives equations of motion for topological static spherically symmetric solutions in (R,G) gravity, finds a new solution for a specific model, and explores black hole thermodynamics and electromagnetic coupling.

Contribution

It provides the first derivation of equations of motion for these solutions in (R,G) gravity and introduces a novel solution for the model (R,G)=R+\u221a{G}.

Findings

New topological solution for (R,G)=R+0G.

Analysis of black hole thermodynamics in this framework.

Coupling with electromagnetic field yields Maxwell solutions.

Abstract

The Lagrangian derivation of the Equations of Motion for topological static spherically symmetric metrics in $\mathcal F (R,G)$-modified gravity is presented and the related solutions are discussed. In particular, a new topological solution for the model $\mathcal F (R,G)=R+\sqrt{G}$ is found. The black hole solutions and the First Law of thermodynamic are analyzed. Furthermore, the coupling with electromagnetic field is also considered and a Maxwell solution is derived.