Regular black holes in quadratic gravity

Berej, W.; Matyjasek, Jerzy; Tryniecki, Dariusz; Woronowicz, Mariusz

doi:10.1007/s10714-006-0270-9

Cited by 137 publications

(115 citation statements)

References 42 publications

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“…But near the center the solution tended to a de Sitter core solution. Subsequently, there has been enormous development in investigating the properties of regular black hole solutions [9][10][11][12][13][14][15][16][17], but most of these regular black hole solutions are more or less based on Bardeen's proposal. In particular, an interesting proposal is made by Hayward [17] for the formation and evaporation of regular black holes, in which the static region is the Bardeen-like black hole.…”

Section: Introductionmentioning

confidence: 99%

Radiating Kerr-like regular black hole

2015

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We derive a radiating regular rotating black hole solution, radiating Kerr-like regular black hole solution. We achieve this by starting from the Hayward regular black hole solution via a complex transformation suggested by Newman-Janis. The radiating Kerr metric, the Kerr-like regular black hole and the standard Kerr metric are regained in the appropriate limits. The structure of the horizon-like surfaces are also determined.

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Section: Introductionmentioning

confidence: 99%

Radiating Kerr-like regular black hole

2015

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“…It also includes (B) nonrotating regular black holes [11][12][13][14][15][16][17] and their rotating counterparts [19][20][21] as well as some nonrotating black holes of f (R) and f (T ) gravities [22,23].…”

Section: Generalizing the Ansatzmentioning

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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“…Presented in the literature results obtained for particular asymptotically flat regular black hole solutions described by metrics of the Kerr-Schild class, confirm the appearance of a temperature maximum and phase transition during evaporation for magnetically charged regular black holes [41][42][43], for the minimal model proposed by Hayward [44,45], for the Hayward and noncommutative [46] regular black holes [47], for charged AdS black holes with a global monopole [48], for the Bardeen black hole [49] which represents the nonlinear magnetic monopole [50], for the Hayward, Ayon-Beato and Garcia [51] black holes [52,53], and for regular black hole in quadratic gravity [52,54].…”

Section: Introductionmentioning

confidence: 99%

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

Dymnikova

2018

Universe

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Abstract:We present a systematic review of thermodynamics of horizons in regular spherically symmetric spacetimes of the Kerr-Schild class, ds 2 = g(r)dt 2 − g −1 (r)dr 2 − r 2 dΩ 2 , both asymptotically flat and with a positive background cosmological constant λ. Regular solutions of this class have obligatory de Sitter center. A source term in the Einstein equations satisfies T t t = T r r and represents an anisotropic vacuum dark fluid (p r = −ρ), defined by the algebraic structure of its stress-energy tensor, which describes a time-evolving and spatially inhomogeneous, distributed or clustering, vacuum dark energy intrinsically related to space-time symmetry. In the case of two vacuum scales it connects smoothly two de Sitter vacua, 8πGTIn the range of the mass parameter M cr1 ≤ M ≤ M cr2 it describes a regular cosmological black hole directly related to a vacuum dark energy. Space-time has at most three horizons: a cosmological horizon r c , a black hole horizon r b < r c , and an internal horizon r a < r b , which is the cosmological horizon for an observer in the internal R-region asymptotically de Sitter as r → 0. Asymptotically flat regular black holes (λ = 0) can have at most two horizons, r b and r a . We present the basic generic features of thermodynamics of horizons revealed with using the Padmanabhan approach relevant for a multi-horizon space-time with a non-zero pressure. Quantum evaporation of a regular black hole involves a phase transition in which the specific heat capacity is broken and changes sign while a temperature achieves its maximal value, and leaves behind the thermodynamically stable double-horizon (r a = r b ) remnant with zero temperature and positive specific heat. The mass of objects with the de Sitter center is generically related to vacuum dark energy and to breaking of space-time symmetry. In the cosmological context space-time symmetry provides a mechanism for relaxing cosmological constant to a certain non-zero value. We discuss also observational applications of the presented results.

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Regular black holes in quadratic gravity

Cited by 137 publications

References 42 publications

Radiating Kerr-like regular black hole

Radiating Kerr-like regular black hole

Vacuum and nonvacuum black holes in a uniform magnetic field

Generic Features of Thermodynamics of Horizons in Regular Spherical Space-Times of the Kerr-Schild Class

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