Cotton Double Copy for Gravitational Waves

TL;DR

This paper establishes a novel double copy relation in three-dimensional topologically massive theories, linking Cotton spinors and dual field strength spinors, extending the concept of the Weyl double copy to curved backgrounds.

Contribution

It introduces the Cotton double copy, a new relation in 3D topologically massive theories, with explicit proofs and examples for Type N spacetimes.

Findings

Cotton double copy relation holds in curved backgrounds.

Explicit proof provided for Type N spacetimes.

Examples demonstrating the Cotton double copy.

Abstract

We construct a double copy relation between the Cotton spinor and the dual field strength spinor of topologically massive theories, as the three-dimensional analogue of the Weyl double copy. The relationship holds in curved backgrounds for wave solutions. We give an explicit proof for Type N spacetimes and show examples satisfying the Cotton double copy.