On the various aspects of electromagnetic potentials in spacetimes with symmetries

Smolić, Ivica

doi:10.1088/0264-9381/31/23/235002

Cited by 10 publications

(13 citation statements)

References 41 publications

(84 reference statements)

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“…Since here we don't need the notion of the angular momentum J, the resulting generalized Smarr formula for the static black holes remains valid even if the spacetime is not necessarily axially symmetric. Note, however, that in the static non-axially symmetric case we rely on the field equation proof [34,51,52]…”

Section: Geometric Approach To the Generalized Smarr Formulamentioning

confidence: 99%

Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields

Gulin

Smolić

2017

Class. Quantum Grav.

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We present a direct, geometric derivation of the generalized Smarr formula for the stationary axially symmetric black holes with nonlinear electromagnetic fields. The additional term is proven to be proportional to the integral of the trace of the electromagnetic energy-momentum tensor and can be written as a product of two conjugate variables. From the novel relation we can deduce all previously proposed forms of the generalized Smarr formula, which were derived only for the spherically symmetric black holes, and provide the lowest order quantum correction to the classical relation from the Euler-Heisenberg Lagrangian. We use adjective "geometric" just to emphasize that in these derivations auxiliary physical assumptions are avoided by the approach based on the quantities of geometric origin.

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Section: Geometric Approach To the Generalized Smarr Formulamentioning

confidence: 99%

Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields

Gulin

Smolić

2017

Class. Quantum Grav.

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“…but only valid for h ∈ {0, 1}. Proceeding by analogy with the m = 0 case, we now Ansatz 20) where the dependence of the additional Θ factor on the coordinates (t, r, φ) is fixed to be Φ h (r)Ψ m (φ) in order to ensure that the potential A EM h,m (U h,m , V h,m , T h,m ) is still an SL(2, R) highest-weight U(1)-eigenstate. Again, note that this is a nonlinear superposition in θ because the functions U h,m (θ), V h,m (θ) need not be identical to the functions P h,m (θ), S h,m (θ) introduced in sections 3 and 4.…”

Section: Derivation Of Electromagnetic Type Solutionsmentioning

confidence: 99%

“…The upshot of this analysis is that force-free solutions with collinear currents can be linearly superposed. Other interesting implications of current collinearity in FFE have been explored in [20].…”

Section: B Principle Of Superposition For Collinear Solutions Of Ffe ...mentioning

confidence: 99%

Exact solutions for extreme black hole magnetospheres

Lupsasca¹,

Rodríguez²

2015

J. High Energ. Phys.

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We present new exact solutions of Force-Free Electrodynamics (FFE) in the Near-Horizon region of an Extremal Kerr black hole (NHEK) and offer a complete classification of the subset that form highest-weight representations of the spacetime's SL(2, R) × U(1) isometry group. For a natural choice of spacetime embedding of this isometry group, the SL(2, R) highestweight conditions lead to stationary solutions with non-trivial angular dependence, as well as axisymmetry when the U(1)-charge vanishes. In addition, we unveil a hidden SL(2, C) symmetry of the equations of FFE that stems from the action of a complex automorphism group, and enables us to generate an SL(2, C) family of (generically time-dependent) solutions. We then obtain still more general solutions with less symmetry by appealing to a principle of linear superposition that holds for solutions with collinear currents. This allows us to resum the highest-weight primaries and their SL(2, R)-descendants. ♠

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“…Just as in classical electrostatics and magnetostatics, a useful strategy for problem solving is introduction of scalar potentials, whenever this is possible [42][43][44]. Magnetic field 1-form defined with respect to a vector field X a is given by B[X] a ≡ X b * F ba .…”

Section: Scalar Potentialsmentioning

confidence: 99%

Schwarzschild spacetime immersed in test nonlinear electromagnetic fields

Bokulić¹,

Smolić²

2020

Class. Quantum Grav.

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Kerr black hole immersed in test, asymptotically homogeneous magnetic field, aligned along the symmetry axis, is described by Wald's solution. We show how this solution may be generalized for nonlinear electromagnetic models via perturbative approach. Using this technique we find the lowest order correction to Wald's solution on Schwarzschild spacetime in Euler-Heisenberg and Born-Infeld models. Finally, we discuss the problem of highly conducting star in asymptotically homogeneous magnetic field.

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On the various aspects of electromagnetic potentials in spacetimes with symmetries

Cited by 10 publications

References 41 publications

Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields

Generalizations of the Smarr formula for black holes with nonlinear electromagnetic fields

Exact solutions for extreme black hole magnetospheres

Schwarzschild spacetime immersed in test nonlinear electromagnetic fields

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