On slowly rotating black holes and nonlinear electrodynamics

Abstract

We discuss the solution to Einstein's equations for a Lense-Thirring inspired metric describing a slowly rotating black hole coupled to nonlinear electrodynamics. We show that different schemes of rotation for the black hole exist; they depend on a parameter $\gamma$ defining the dependence of the metric on the polar angle. The fulfilment of the complete set of gravitational field equations and conservation laws implies constraints on this parameter and the metric functions. The vanishing of $\gamma$ provides the Lense-Thirring line element associated to any non-linear electrodynamics; the Kerr-Newman metric for slow rotation arises when $\gamma$ is not vanishing, a feature that emphasises the unique role played by Maxwell's electrodynamics.

arXiv comment11 pages

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• Reply to "Comment on 'Greybody radiation and quasinormal modes of Kerr-like black hole in Bumblebee gravity model' "
• Einstein-non-linear Maxwell-Yukawa black hole
• Remarks on a nonlinear electromagnetic extension in AdS Reissner-Nordström spacetime
• Slowly rotating black holes and their scalarization
• The Interiors of Singularity-Free Rotating Black Holes
• Structure and thermodynamics of charged nonrotating black holes in higher dimensions
• Superradiant instability in slowly rotating Kerr-Newman black holes
• Scalarization of slowly rotating black holes