Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions

While the Kerr-Schild double copy of the Coulomb solution in dimensions higher than three is the Schwarzschild black hole, it is known that it should be a non-vacuum solution in three dimensions. We show that the static black hole solution of Einstein-Maxwell theory (with one ghost sign in the actio...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Alkac, Gokhan, Gumus, Mehmet Kemal, Mehmet Ali Olpak
Format: Article
Language:English
Subjects:
Black holes
Cosmological constant
Electric fields
Scalars
Online Access:Get full text
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Summary:While the Kerr-Schild double copy of the Coulomb solution in dimensions higher than three is the Schwarzschild black hole, it is known that it should be a non-vacuum solution in three dimensions. We show that the static black hole solution of Einstein-Maxwell theory (with one ghost sign in the action) is the double copy with the correct Newtonian limit, which provides an improvement over the previous construction with a free scalar field that does not vanish at infinity. By considering a negative cosmological constant, we also study the charged Bañados-Teitelboim-Zanelli black hole and find that the single copy gauge field is the Coulomb solution modified by a term which describes an electric field linearly increasing with the radial coordinate, which is the usual behaviour of the Schwarzschild-AdS black hole in higher dimensions when written around a flat background metric.
ISSN:2331-8422
DOI:10.48550/arxiv.2105.11550