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Slowly rotating black holes in nonlinear electrodynamics

Mar 3, 2022

11 pages

Published in:

Phys.Rev.D 105 (2022) 10, 104064

Published: May 15, 2022

e-Print:

2203.01919 [gr-qc]

DOI:

10.1103/PhysRevD.105.104064 (publication)

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Abstract: (APS)

We show how (at least, in principle) one can construct electrically and magnetically charged slowly rotating black hole solutions coupled to nonlinear electrodynamics (NLE). Our generalized Lense–Thirring ansatz is, apart from the static metric function

f

and the electrostatic potential

ϕ

inherited from the corresponding spherical solution, characterized by two new functions

h

(in the metric) and

ω

(in the vector potential) encoding the effect of rotation. In the linear Maxwell case, the rotating solutions are completely characterized by a static solution, featuring

h = (f - 1) / r^{2}

and

ω = 1

. We show that when the first is imposed, the ansatz is inconsistent with any restricted (see below) NLE but the Maxwell electrodynamics. In particular, this implies that the (standard) Newman–Janis algorithm cannot be used to generate rotating solutions for any restricted nontrivial NLE. We present a few explicit examples of slowly rotating solutions in particular models of NLE, as well as briefly discuss the NLE charged Taub-NUT spacetimes.

Note:

11 pages, no figures v3: slightly extended version, added references

electromagnetic field: nonlinear
black hole: rotation
charge: electric
charge: magnetic
solution: static
potential: electrostatic
space-time: Taub-NUT
potential: vector
rotation: effect
black hole: charge

References(73)

Figures(0)

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