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 Li\'enard-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.
Cite
@article{arxiv.1910.04197,
title = {Kerr-Schild Double Copy and Complex Worldlines},
author = {Ibrahima Bah and Ross Dempsey and Peter Weck},
journal= {arXiv preprint arXiv:1910.04197},
year = {2020}
}
Comments
To be published in JHEP. Version updated in include clarifications in wording, new sentences making a few additional remarks, and typo corrections