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Register a new userRegular black holes in $f(G)$ gravity
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Added by
Marcos Vinicius de Sousa Silva
Publication date
2018
fields
Physics
and research's language is
English
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In this work, we study the possibility of generalizing solutions of regular black holes with an electric charge, constructed in general relativity, for the $f(G)$ theory, where $G$ is the Gauss-Bonnet invariant. This type of solution arises due to the coupling between gravitational theory and nonlinear electrodynamics. We construct the formalism in terms of a mass function and it results in different gravitational and electromagnetic theories for which mass function. The electric field of these solutions are always regular and the strong energy condition is violated in some region inside the event horizon. For some solutions, we get an analytical form for the $f(G)$ function. Imposing the limit of some constant going to zero in the $f(G)$ function we recovered the linear case, making the general relativity a particular case.
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In this work, we study the existence of regular black holes solutions with multihorizons in general relativity and in some alternative theories of gravity. We consider the coupling between the gravitational theory and nonlinear electrodynamics. The coupling generates modifications in the electromagnetic sector. This paper has as main objective generalize solutions already known from general relativity to the $f(G)$ theory. To do that, we first correct some misprints of the Odintsov and Nojiris work in order to introduce the formalism that will be used in the $f(G)$ gravity. In order to satisfy all field equations, the method to find solutions in alternative theories generates different $f(R)$ and $f(G)$ functions for each solution, where only the nonlinear term of $f(G)$ contributes to the field equations. We also analyze the energy conditions, since it is expected that some must be violated to find regular black holes, and using an auxiliary field, we analyze the nonlinearity of the electromagnetic theory.
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