Kerr-Schild double copy of the Coulomb solution in three dimensions
Gökhan Alkaç, Mehmet Kemal Gümüş, Mehmet Ali Olpak
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 nonvacuum 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 Ba\~nados-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 behavior of the Schwarzschild-AdS black hole in higher dimensions when written around a flat background metric.