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<p>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 <i>ρ</i> = −<i>θ</i> − <i>iω</i>, 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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年5月21日

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  • Damien A. Easson,
  • Michael J. Falato

摘要

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.