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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• The instabilities and (anti)-evaporation of Schwarzschild-de Sitter black holes in modified gravity
• How a conformally flat (GR)4 impacts Gauss-Bonnet gravity?
• First law of thermodynamics and entropy of FLRW universe in modified gravity
• Reconstructions of $f(\mathcal{P})$ and $f(\mathcal{Q})$ gravity models from $(m,n)$-type Barrow Holographic Dark Energy: Analysis and Observational Constraints
• Black holes with constant topological Euler density
• Reconstructions of Einstein-Aether Gravity from Barrow Agegraphic and New Barrow Agegraphic Dark Energy models: Examinations and Observational Limits
• Study of Some Cosmological Parameters for Interacting New Holographic Dark Energy Model in f(T) Gravity
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• Thermodynamical aspects of black holes in modified gravity
• Gauss-Bonnet Gravity in $D=4$ Without Gauss-Bonnet Coupling to Matter - Cosmological Implications