Kerr-Schild double copy and complex worldlines

Abstract

We use the classical double copy to identify a necessary condition for Maxwell theory sources to constitute single copies of Kerr-Schild solutions to Einstein’s equations. In the case of four-dimensional Kerr-Schild spacetimes on Minkowski backgrounds, we extend this condition to a parameterization of the corresponding single copies. These are given by Líenard-Wiechert fields of charges on complex worldlines. This unifies the known instances of the Kerr-Schild double copy black holes on flat four-dimensional backgrounds into a single framework. Furthermore, we use the more generic condition identified to show why the black ring in five dimensions does not admit Kerr-Schild coordinates.

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Correspondence to Ross Dempsey.

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ArXiv ePrint: 1910.04197

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Bah, I., Dempsey, R. & Weck, P. Kerr-Schild double copy and complex worldlines. J. High Energ. Phys. 2020, 180 (2020). https://doi.org/10.1007/JHEP02(2020)180

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Keywords

  • Black Holes
  • Classical Theories of Gravity
  • Gauge-gravity correspondence