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.
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Acknowledgments
L.S. thanks Dr. Roberto Di Criscienzo and Prof. Guido Cognola for help and valuable suggestions and would like to appreciate the hospitality at Eurasian National University where the work was developed.
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Myrzakulov, R., Sebastiani, L. & Zerbini, S. Topological static spherically symmetric vacuum solutions in gravity \(\mathcal{F }(R,G)\) . Gen Relativ Gravit 45, 675–690 (2013). https://doi.org/10.1007/s10714-012-1493-6
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DOI: https://doi.org/10.1007/s10714-012-1493-6