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arXiv · 2004.07560

Stability of magnetic black holes in general nonlinear electrodynamics

Kimihiro Nomura·Daisuke Yoshida·Jiro Soda
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Abstract

We study the perturbative stability of magnetic black holes in a general class of nonlinear electrodynamics, where the Lagrangian is given by a general function of the field strength of electromagnetic field $F_{\mu\nu}$ and its Hodge dual $\widetilde{F}_{\mu\nu}$. We derive sufficient conditions for the stability of the black holes. We apply the stability conditions to Bardeen's regular black holes, black holes in Euler-Heisenberg theory, and black holes in Born-Infeld theory. As a result, we obtain a sufficient condition for the stability of Bardeen's black holes, which restricts $F_{\mu\nu}\widetilde{F}^{\mu\nu}$ dependence of the Lagrangian. We also show that black holes in Euler-Heisenberg theory are stable for a sufficiently small magnetic charge. Moreover, we prove the stability of black holes in the Born-Infeld electrodynamics even when including $F_{\mu\nu}\widetilde{F}^{\mu\nu}$ dependence.

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Kimihiro Nomura, Daisuke Yoshida, Jiro Soda. 2020-04-16. Stability of magnetic black holes in general nonlinear electrodynamics. https://doi.org/10.1103/physrevd.101.124026

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