Abstract
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.
Highlights
Since it was proposed, general relativity has been tested and proved to be quite effective to describe phenomena in the solar system and beyond [1,2,3]
If we analyze the components of Tμν we find some kind of anisotropic matter/field, that is very similar to the nonlinear electrodynamics
We have developed a method that generalizes solutions of regular black holes, already known from general relativity, to the f (G) theory
Summary
General relativity has been tested and proved to be quite effective to describe phenomena in the solar system and beyond [1,2,3]. Where L(F) is the Lagrangian density of the nonlinear electrodynamics, f (G) represents a general function of the Gauss–Bonnet invariant, G = R2 − 4Rμν Rμν + Rμναβ Rμναβ , with R being the curvature scalar, Rμν is the Ricci tensor and Rμναβ is the Riemann tensor and g is the determinant of the metric gμν. In the way that the equations of motion are written, the effective energy density and the effective pressures are equal to the components of Einstein tensor. In this sense, if we consider the same metric, the energy conditions in general relativity and f (G) gravity will be the same.
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