Untwisting the double copy: the zeroth copy as an optical seed

TL;DR

This paper links optical geometry with the double-copy framework, showing how a complex seed encodes Kerr--Schild spacetimes and gauge fields without twistor methods.

Contribution

It introduces a spacetime realization of the zeroth copy using a complex optical seed, connecting optical geometry with double-copy constructions.

Findings

The complex optical seed is harmonic and reconstructs the congruence algebraically.

The seed's real part gives the Kerr--Schild profile, and its gradient yields the gauge-field strength.

Provides a geometric interpretation of the zeroth copy without twistor methods.

Abstract

We present a historical optical foundation for stationary vacuum Kerr--Schild spacetimes on a flat background and interpret it in modern double-copy language. In this setting, a complex optical seed \(\rho=-\theta-i\omega\), built from the expansion and signed twist of the Kerr--Schild congruence, is harmonic, while its inverse obeys an eikonal equation and reconstructs the congruence algebraically. Thus the local stationary geometry is organized by a single complex seed. In the overlap of the stationary Kerr--Schild and Petrov type--D Weyl double-copy framework, this seed furnishes a normalized representative of the zeroth-copy data, while its real part yields the Kerr--Schild profile and its gradient generates the single-copy gauge-field strength. The construction provides, without recourse to twistor methods, a spacetime realization of how a single complex seed builds the congruence, organizes the associated spacetime and gauge fields, and encodes the geometric content of the zeroth copy.