Kerr-Schild double copy of the Coulomb solution in three dimensions


ALKAÇ G., GÜMÜŞ M. , Olpak M. A.

PHYSICAL REVIEW D, vol.104, no.4, 2021 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 104 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1103/physrevd.104.044034
  • Title of Journal : PHYSICAL REVIEW D

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 Banados-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.