Regular black holes in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math>gravity coupled to nonlinear electrodynamics

Rodrigues, Manuel E.; Ednaldo, L. B.; Marques, Glauber Tadaiesky; Zanchin, Vilson T.

doi:10.1103/physrevd.94.024062

Cited by 70 publications

(49 citation statements)

References 127 publications

(107 reference statements)

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“…In general relativity, from the condition G 0 0 − G 1 1 = 0 in the Einstein tensor, we have that a + b = 0. In alternatives theories of gravity, it's not necessarily the truth, for example, in the f (R) theory it's is just one of the possibilities [73][74][75]. If we subtract (9) from (10) we get…”

Section: Nonlinear Electrodynamics Coupled With F (G) Gravity: Equatimentioning

confidence: 99%

“…Therefore, the electric field goes to zero at the infinity as in general relativity and different of the f (R) gravity [74,75]. Now we will check if the solution satisfies the energy conditions.…”

Section: First Regular Solutionmentioning

confidence: 99%

“…If we have = 0 the electric field is well behaved. In f (R) theory, due to the coupled between the gravity and the electromagnetic theory, the electric field diverges at the infinity of the radial coordinate [74,75], that not necessary happen in the f (G) theory.…”

Section: Reissner-nordström-anti-de Sitter Casementioning

confidence: 99%

“…After Bardeen's proposal, several regular solutions were studied in the literature. Most of these were developed in general relativity [57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72], others in f (R) theory [73][74][75] and f (T ) theory [76]. In Einstein's theory it is also possible to find solutions with rotation [77][78][79][80][81][82][83] and even with several horizons [84], solutions with multihorizons are also studied in alternative theories of gravity.…”

Section: Introductionmentioning

confidence: 99%

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Regular black holes in f(G) gravity

Silva

Rodrigues

2018

Eur. Phys. J. C

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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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Section: Nonlinear Electrodynamics Coupled With F (G) Gravity: Equatimentioning

confidence: 99%

Section: First Regular Solutionmentioning

confidence: 99%

Section: Reissner-nordström-anti-de Sitter Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Regular black holes in f(G) gravity

Silva

Rodrigues

2018

Eur. Phys. J. C

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“…In fact, this effect, which was masked by the approximation made in (3), exists for all nonvacuum charged black holes no matter the nature of the stress-energy is. In our restriction (11), this effect has been derived in the linear case (15) but it should apply to neutral or charged generic configurations too where f expands as f 1 r + f 2 + power series in 1/r , as are the cases with the Ayón-Beato-García static black hole [12], the solutions derived in [17,24], and the black holes of the f (T ) [23] and f (R) [25] gravities. 3.…”

Section: The Nonrotating Case: a =mentioning

confidence: 99%

Vacuum and nonvacuum black holes in a uniform magnetic field

Azreg‐Aïnou

2016

Eur. Phys. J. C

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We modify and generalize the known solution for the electromagnetic field when a vacuum, stationary, axisymmetric black hole is immersed in a uniform magnetic field to the case of nonvacuum black holes (of modified gravity) and determine all linear terms of the vector potential in powers of the magnetic field and the rotation parameter. The magnetic field problemA Killing vector ξ μ in vacuum (no stress-energy T μν ≡ 0) is endowed with the property of being parallel, that is, proportional, to some vector potential A μ that solves the sourceless (no currentsMaxwell field equations. So, ξ μ is itself a solution to the same source-less Maxwell field equations. In Ref.[1], this property was employed as an ansatz to determine the electromagnetic field of a vacuum, stationary, axisymmetric, asymptotically flat black hole placed in a uniform magnetic field that is asymptotically parallel to the axis of symmetry. The ansatz stipulates that the vector potential of the solution be in the plane spanned by the timelike Killing vector ξ μ t = (1, 0, 0, 0) and spacelike one ξ μ ϕ = (0, 0, 0, 1) of the stationary, axisymmetric black hole,Since ξ μ t and ξ μ ϕ are pure geometric objects, they do not encode information on the applied magnetic field B; such information is encoded in the coefficients (C t , C ϕ ). Here B is taken as a test field, so the metric of the stationary, axisymmetric black hole too does not encode any information on the applied magnetic field.In this work, a spacetime metric has signature (+, −, −, −) and andrespectively, 1 where B and Q are seen as perturbations, that is, if the metric of the background black hole is that of Kerr, then Qξ t μ /(2M) is, up to an additive constant, the one-form A μ dx μ = −Qr(dt − a sin 2 θ dϕ)/ρ 2 of the Kerr-Newman black hole (with ρ 2 = r 2 + a 2 cos 2 θ ). It is important to emphasize this point: the potential given by (1) and (3) is not an exact solution to the source-less Maxwell equations,if the background metric is that of the charged black hole itself. Rather, it is a solution to (4) if the background metric is that of the corresponding uncharged black hole. For instance, in the Kerr background metric, the potential given by (1) and (3) is a solution to (4), but in the KerrNewman background metric the nonvanishing electric charge density J t and the ϕ current density J ϕ expand in powers of Q aswhich are zero to first order only. Even if rotation is suppressed (a = 0), J t is still nonzero:and its integral charge is also nonzero. Where does this electric charge density come from (the only existing electric 1 The sign "+" in (3) in front of Q is due to our metric-signature choice.123

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f(R) Gravity in a Kaluza–Klein Theory with Degenerate Metric

Searight¹

2020

Found Phys

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Regular black holes inf(R)gravity coupled to nonlinear electrodynamics

Cited by 70 publications

References 127 publications

Regular black holes in f(G) gravity

Regular black holes in f(G) gravity

Vacuum and nonvacuum black holes in a uniform magnetic field

f(R) Gravity in a Kaluza–Klein Theory with Degenerate Metric

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