Rotating magnetic solution in three dimensional Einstein gravity

Dias, Óscar J. C.; Lemos, José P. S.

doi:10.1088/1126-6708/2002/01/006

Cited by 78 publications

(86 citation statements)

References 16 publications

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“…[11] and [14,15] regularize these divergences by taking into account a boundary contribution or by the introduction of a topological ChernSimons term respectively. We note also that the magnetic solution (4) has been extended in order to include (i) angular momentum, (ii) the definition of conserved quantities, (iii) upper bounds for the conserved quantities themselves, and (iv) a new interpretation for the magnetic field source [16].…”

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confidence: 99%

Azimuthal electric field in a static rotationally symmetric (2+1)-dimensional spacetime

Cataldo¹

2002

Physics Letters B

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The fundamental metrics, which describe any static three-dimensional Einstein-Maxwell spacetime (depending only on a unique spacelike coordinate), are found. In this case there are only three independent components of the electromagnetic field: two for the vector electric field and one for the scalar magnetic field. It is shown that we can not have any superposition of these components of the electric and magnetic fields in this kind of static gravitational field. One of the electrostatic Einstein-Maxwell solutions is related to the magnetostatic solution by a duality mapping, while the second electrostatic gravitational field must be solved separately. Solutions induced by the more general (2+1)-Maxwell tensor on the static cylindrically symmetric spacetimes are studied and it is shown that all of them are also connected by duality mappings. whereHere, the solution has radial electric and magnetic fields given by E(r) = q e /r 2 and B(r) = q m /r 2 respectively. The case q m = 0 describes a rest charge at the origin of spherical coordinates and q e = 0 may be interpreted as a magnetic monopole. The magnetically charged Reissner-Nordström solution is connected to the electrically charged solution, since all the cases with an electric field without sources can be reformulated to be the corresponding cases with a magnetic field (dual to the initial electric one) or mixtures of both fields (through a duality rotation). In all these cases the form of the metric is the same.The Einstein-Maxwell theories in (2+1)-dimensions without cosmological constant have been discussed by several authors [2,3,4]. In [4] the authors found the first three-dimensional static electrically charged space-time. Later the inclusion of the cosmological constant was considered. In (2+1)-dimensions there exist the electric and magnetic analogs to the Reissner-Nordström-Kottler solution. They are the static Bañados-Teitelboim-Zanelli * mcataldo@ubiobio.cl (BTZ) black hole (E = q e /r) [5]and the Hirschmann-Welch (HW) magnetic solutionis the electric charge, q m magnetic charge and M is the mass of the BTZ black hole. Both solutions are asymptotically anti-de Sitter, like the Reissner-Nordström-Kottler solution for Λ < 0. In Ref. [7] it is shown that the both solutions (3) and (4) are connected by a duality transformation. Rotating (2+1)-Einstein-Maxwell solutions have been obtained by several authors using an appropriate coordinate transformation [8,9]. Others solutions also have been obtained assuming selfdual (or anti-self-dual) condition imposed on the orthonormal basis components of the electric and magnetic fields [10,11,12]. Note that the presence of divergences at spatial infinity in the mass and angular momentum is an usual feature in electrically charged solutions [13]. The authors of the Ref. [11] and [14, 15] regularize these divergences by taking into account a boundary contribution or by the introduction of a topological ChernSimons term respectively. We note also that the magnetic solution (4) has been extended in order to incl...

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confidence: 99%

Azimuthal electric field in a static rotationally symmetric (2+1)-dimensional spacetime

Cataldo¹

2002

Physics Letters B

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“…The conical singularity can be removed if one exchanges the coordinate ϕ with the following period (53) where μ is given by…”

Section: Geometric Propertiesmentioning

confidence: 99%

“…Due to these facts, investigation of (2+1)-dimensional spacetimes is important. Three dimensional solutions of black holes and magnetic solutions have been studied by many authors [50][51][52][53][54][55][87][88][89][90][91][92][93]. This tremendous interest in these solutions is due to fact that three dimensional solutions contribute fundamentally to conceptual issues of astrophysical subjects such as black holes thermodynamics [94][95][96].…”

Section: Introductionmentioning

confidence: 99%

Three dimensional nonlinear magnetic AdS solutions through topological defects

et al. 2015

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Inspired by large applications of topological defects in describing different phenomena in physics, and considering the importance of three dimensional solutions in AdS/CFT correspondence, in this paper we obtain magnetic anti-de Sitter solutions of nonlinear electromagnetic fields. We take into account three classes of nonlinear electrodynamic models; first two classes are the well-known BornInfeld like models including logarithmic and exponential forms and third class is known as the power Maxwell invariant nonlinear electrodynamics. We investigate the effects of these nonlinear sources on three dimensional magnetic solutions. We show that these asymptotical AdS solutions do not have any curvature singularity and horizon. We also generalize the static metric to the case of rotating solutions and find that the value of the electric charge depends on the rotation parameter. Finally, we consider the quadratic Maxwell invariant as a correction of Maxwell theory and we investigate the effects of nonlinearity as a correction. We study the behavior of the deficit angle in presence of these theories of nonlinearity and compare them with each other. We also show that some cases with negative deficit angle exists which are representing objects with different geometrical structure. We also show that in case of the static only magnetic field exists whereas by boosting the metric to rotating one, electric field appears too.

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“…In the present work, we use the generalisation to the rotating case as formulated by Dias and Lemos [33], whereby the line element is in the form…”

Section: Ads Black Holes and The Magnetic Solution To The (2 + 1) Einmentioning

confidence: 99%

Energy and Momentum Distributions of the Magnetic Solution to (2+1) Einstein–maxwell Gravity

Grammenos

2005

Mod. Phys. Lett. A

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We use Møller's energy-momentum complex in order to explicitly evaluate the energy and momentum density distributions associated with the three-dimensional magnetic solution to the Einstein-Maxwell equations. The magnetic spacetime under consideration is a one-parametric solution describing the distribution of a radial magnetic field in a three-dimensional AdS background, and representing the superposition of the magnetic field with a 2+1 Einstein static gravitational field.

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Rotating magnetic solution in three dimensional Einstein gravity

Cited by 78 publications

References 16 publications

Azimuthal electric field in a static rotationally symmetric (2+1)-dimensional spacetime

Azimuthal electric field in a static rotationally symmetric (2+1)-dimensional spacetime

Three dimensional nonlinear magnetic AdS solutions through topological defects

Energy and Momentum Distributions of the Magnetic Solution to (2+1) Einstein–maxwell Gravity

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