Bardeen regular black hole with an electric source

Abstract

If some energy conditions on the stress-energy tensor are violated, is possible construct regular black holes in General Relativity and in alternative theories of gravity. This type of solution has horizons but does not present singularities. The first regular black hole was presented by Bardeen and can be obtained from Einstein equations in the presence of an electromagnetic field. E. Ayon-Beato and A. Garcia reinterpreted the Bardeen metric as a magnetic solution of General Relativity coupled to a nonlinear electrodynamics. In this work show that the Bardeen model may also be interpreted as a solutions of Einstein equations in the presence of a electric source, whose electric field does not behaves as a Coulomb field. We analyzed the asymptotic forms of the Lagrangian for the electric case and also analyzed the energy conditions.

Deflection angle of photon from magnetized black hole and effect of nonlinear electrodynamics

“…In general theory of gravity, spacetime singularities raise a number of problems, both mathematical and physical [42][43][44][45][46][47][48][49][50]. Using the nonlinear electrodynamics it is possible to remove these singularities by constructing a regular black hole solution [51][52][53][54][55]. Recently, Kruglov has proposed a new model of nonlinear electrodynamics with two parameters β and γ where the the specific range of magnetic field, the causality and unitary principles are satisfied [41].…”

Regular black holes in f(G) gravity

“…The Bardeen metric has a de Sitter core with an equation of state ρ = −p, where ρ is the energy density and p is the pressure. This solution also satisfies the weak energy condition and violates de strong energy condition [55,56]. Since this solution does not satisfy Einstein equations in vacuum, Ayón-Beato and Garcia have shown that the Bardeen solution can be obtained through Einstein equations with a nonlinear magnetic source [55].…”

“…Since this solution does not satisfy Einstein equations in vacuum, Ayón-Beato and Garcia have shown that the Bardeen solution can be obtained through Einstein equations with a nonlinear magnetic source [55]. It is also possible to show that this metric is a solution for the case with a nonlinear electrical source, but in this case, it is not possible to obtain a closed form for the electromagnetic Lagrangian [56]. After Bardeen's proposal, several regular solutions were studied in the literature.…”

Electrically charged black holes in linear and nonlinear electrodynamics: Geodesic analysis and scalar absorption

“…The NED generalizes Maxwell's theory [13][14][15] and appears at certain energy levels of some string/M theories [16][17][18]. Based on a NED framework, several electrically [19][20][21][22][23] and magnetically [24][25][26][27][28] charged RBH solutions have been proposed, as well as NED-based RBH solutions in alternative theories of gravity [29,30].…”