Type D Spacetimes and the Weyl Double Copy

TL;DR

This paper introduces the Weyl double copy, a new relation linking curvature in type D vacuum spacetimes to electromagnetic fields, unifying and extending previous double copy approaches with novel examples like the C-metric.

Contribution

It presents the Weyl double copy for all type D vacuum spacetimes, resolving ambiguities in earlier methods and providing new insights into classical solutions such as the C-metric and Eguchi-Hanson instanton.

Findings

Weyl double copy relates spacetime curvature to electromagnetic fields.

The C-metric maps to the Lienard-Wiechert potential for accelerated charges.

A new interpretation of the Eguchi-Hanson instanton is provided.

Abstract

We study the double-copy relation between classical solutions in gauge theory and gravity, focusing on four-dimensional vacuum metrics of algebraic type D, a class that includes several important solutions. We present a double copy of curvatures that applies to all spacetimes of this type -- the Weyl double copy -- relating the curvature of the spacetime to an electromagnetic field strength. We show that the Weyl double copy is consistent with the previously known Kerr-Schild double copy, and in fact resolves certain ambiguities of the latter. The most interesting new example of the classical double copy presented here is that of the C-metric. This well-known solution, which represents a pair of uniformly accelerated black holes, is mapped to the Lienard-Wiechert potential for a pair of uniformly accelerated charges. We also present a new double-copy interpretation of the Eguchi-Hanson instanton.