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Electromagnetic field and cosmic censorship

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Abstract

We construct a gedanken experiment in which an extremal Kerr black hole interacts with a test electromagnetic field. Using Teukolsky’s solutions for electromagnetic perturbations in Kerr spacetime, and the conservation laws imposed by the energy momentum tensor of the electromagnetic field and the Killing vectors of the spacetime, we prove that this interaction cannot convert the black hole into a naked singularity, thus cosmic censorship conjecture is not violated in this case.

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Notes

  1. However, all the relations starting with Eq. (2), including the separation and the asymptotic solutions, are meaningful/valid for the Kerr–Newman metric (which is also of Petrov type D) as well, since the latter is obtained from Kerr by replacing \(\Delta \) with \(r^2-2Mr+a^2+Q^{2}\) (where \(Q^{2}\) can be \(Q_{e}^{2}+Q_{m}^{2}\) if the black hole has electric charge \(Q_{e}\) and magnetic charge \(Q_{m}\)); in other words, \(Q\) does not appear outside \(\Delta \), including the derivatives of \(\Delta \). Hence it does not appear in the derivatives of the metric, where it might have other contribution to the field equations. On the other hand, the electromagnetic field carries no charge, hence the free field will not couple to the field of the black hole, so no \(Q\) terms will come from there either.

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Acknowledgments

I would like to thank İ Semiz for helpful discussions and comments.

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  1. Department of Physics, Boğaziçi University, Bebek, 34342 , Istanbul, Turkey

    Koray Düztaş

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  1. Koray Düztaş
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Correspondence to Koray Düztaş.

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Düztaş, K. Electromagnetic field and cosmic censorship. Gen Relativ Gravit 46, 1709 (2014). https://doi.org/10.1007/s10714-014-1709-z

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