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A bstract 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 ρ = − θ − iω , 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.
Easson et al. (Thu,) studied this question.
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