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

Abstract

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.

arXiv comment15 pages + references, typos in equations (3.1) and (3.3) corrected, minor changes, version to appear in PRD (with three additional references)

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Cited by in corpus (22)

• Asymptotic Weyl Double Copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Alternative formulations of the twistor double copy
• The double copy of the multipole expansion
• Why is the Weyl double copy local in position space?
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• New framework for classical double copies
• Classical double copy in the black hole mini-superspace
• Massive Covariant Colour-Kinematics in 3D
• NS-NS Spacetimes from Amplitudes