New framework for classical double copies

TL;DR

This paper introduces a new framework for classical double copies in gravity, using Killing vectors, and demonstrates its effectiveness with the Kasner metric, extending the scope of exact double copy solutions.

Contribution

It proposes a novel metric-level framework for classical double copies and provides the first flat-space type-I Weyl double copy example for an algebraically general spacetime.

Findings

Established a new method for generating classical double copies using Killing vectors.

Provided the first flat-space type-I Weyl double copy for the Kasner metric.

Confirmed the double copy at the curvature level for a non-algebraically special spacetime.

Abstract

The double copy relates gauge and gravitational theories, with widespread application to quantum scattering amplitudes and classical perturbative results. It also connects exact classical solutions of Abelian gauge and gravitational theories in a small number of specific examples, known as classical double copies. These have a number of special properties, such as being algebraically special, and it remains an open question whether examples exist for algebraically general spacetimes or with nontrivial dynamics. Here we provide a novel framework for understanding classical double copies at the level of the metric, both organizing the known examples and exploring their properties under a new lens. Utilizing Killing vectors as natural gauge fields on a spacetime, we propose a procedure for generating new classical double copies. As a proof of concept, we provide a flat-space single copy for the Kasner metric, an algebraically general spacetime. This example is also a double copy at the level of its curvature, and provides the first type-$I$ Weyl double copy on flat spacetime, confirming expectations from perturbation theory. This provides a promising avenue for extending exact double copies to a broader class of general, physically relevant spacetimes.