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

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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.

fields

gr-qc 1

years

2026 1

verdicts

UNVERDICTED 1

representative citing papers

Birkhoff rigidity from a covariant optical seed

gr-qc · 2026-04-10 · unverdicted · novelty 7.0

Spherical symmetry in stationary vacuum gravity forces the optical seed to equal the inverse areal radius, making Schwarzschild the unique nowhere-vanishing optical-seed Kerr-Schild geometry.

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  • Birkhoff rigidity from a covariant optical seed gr-qc · 2026-04-10 · unverdicted · none · ref 15 · internal anchor

    Spherical symmetry in stationary vacuum gravity forces the optical seed to equal the inverse areal radius, making Schwarzschild the unique nowhere-vanishing optical-seed Kerr-Schild geometry.