Kerr-Schild Double Copy and Complex Worldlines

TL;DR

This paper explores the classical double copy correspondence between Maxwell and Kerr-Schild solutions in general relativity, revealing conditions for single copies and unifying known black hole solutions within this framework.

Contribution

It identifies a necessary condition for Maxwell sources to be single copies of Kerr-Schild solutions and extends this to complex worldlines, unifying various Kerr-Schild black holes.

Findings

Derived a condition linking Maxwell sources to Kerr-Schild solutions.

Unified Kerr-Schild black holes on flat backgrounds within a single framework.

Explained why the five-dimensional black ring lacks Kerr-Schild coordinates.

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.