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arXiv · 1804.05846

On the existence of the Blandford-Znajek monopole for a slowly rotating Kerr black hole

Gianluca Grignani·Troels Harmark·Marta Orselli
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Abstract

The Blandford-Znajek monopole is a conjectured solution of force-free electrodynamics in the vicinity of a slowly rotating Kerr black hole, supposedly defined as a perturbation in small angular momentum. It is used to argue for the extraction of energy from rotating black holes by the Blandford-Znajek process. We set up a careful analysis of the perturbative definition of the Blandford-Znajek monopole, showing in particular that the regime in which it is defined allows to use the technique of matched asymptotic expansions. Our conclusion is that the Blandford-Znajek monopole, as it is defined, is not consistent with demanding physically reasonable boundary conditions far away from the event horizon. This puts into question the existence of the Blandford-Znajek monopole, at least in the limit of slow rotation of the Kerr black hole.

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Gianluca Grignani, Troels Harmark, Marta Orselli. 2018-10-17. On the existence of the Blandford-Znajek monopole for a slowly rotating Kerr black hole. https://doi.org/10.1103/physrevd.98.084056

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