The Kerr-Schild double copy in Lifshitz spacetime


ALKAÇ G., Gümüş M. K. , Tek M.

Journal of High Energy Physics, vol.2021, no.5, 2021 (Journal Indexed in SCI) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 2021 Issue: 5
  • Publication Date: 2021
  • Doi Number: 10.1007/jhep05(2021)214
  • Title of Journal : Journal of High Energy Physics
  • Keywords: Classical Theories of Gravity, Black Holes, CLASSICAL DOUBLE COPY

Abstract

© 2021, The Author(s).The Kerr-Schild double copy is a map between exact solutions of general relativity and Maxwell’s theory, where the nonlinear nature of general relativity is circumvented by considering solutions in the Kerr-Schild form. In this paper, we give a general formulation, where no simplifying assumption about the background metric is made, and show that the gauge theory source is affected by a curvature term that characterizes the deviation of the background spacetime from a constant curvature spacetime. We demonstrate this effect explicitly by studying gravitational solutions with non-zero cosmological constant. We show that, when the background is flat, the constant charge density filling all space in the gauge theory that has been observed in previous works is a consequence of this curvature term. As an example of a solution with a curved background, we study the Lifshitz black hole with two different matter couplings. The curvature of the background, i.e., the Lifshitz spacetime, again yields a constant charge density; however, unlike the previous examples, it is canceled by the contribution from the matter fields. For one of the matter couplings, there remains no additional non-localized source term, providing an example for a non-vacuum gravity solution corresponding to a vacuum gauge theory solution in arbitrary dimensions.