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

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.

12 pages, minor corrections, published version

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