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Isometries and the double copy

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arxiv 2306.13687 v4 pith:ZW7IHHIP submitted 2023-06-22 gr-qc hep-th

Isometries and the double copy

classification gr-qc hep-th
keywords kerr-schildcopyspacetimedoublevectorspacetimesvacuumkilling
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In the standard derivation of the Kerr-Schild double copy, the geodicity of the Kerr-Schild vector and the stationarity of the spacetime are presented as assumptions that are necessary for the single copy to satisfy Maxwell's equations. However, it is well known that the vacuum Einstein equations imply that the Kerr-Schild vector is geodesic and shear-free, and that the spacetime possesses a distinguished vector field that is simultaneously a Killing vector of the full spacetime and the flat background, but need not be timelike with respect to the background metric. We show that the gauge field obtained by contracting this distinguished Killing vector with the Kerr-Schild graviton solves the vacuum Maxwell equations, and that this definition of the Kerr-Schild double copy implies the Weyl double copy when the spacetime is Petrov type D. When the Killing vector is taken to be timelike with respect to the background metric, we recover the familiar Kerr-Schild double copy, but the prescription is well defined for any vacuum Kerr-Schild spacetime and we present new examples where the Killing vector is null or spacelike. While most examples of physical interest are type D, vacuum Kerr-Schild spacetimes are generically of Petrov type II. We present a straightforward example of such a spacetime and study its double copy structure. Our results apply to real Lorentzian spacetimes as well as complex spacetimes and real spacetimes with Kleinian signature, and provide a simple correspondence between real and self-dual vacuum Kerr-Schild spacetimes. This correspondence allows us to study the double copy structure of a self-dual analog of the Kerr spacetime. We provide evidence that this spacetime may be diffeomorphic to the self-dual Taub-NUT solution.

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Cited by 7 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Mass/electric versus NUT/magnetic charges: duality from scattering amplitudes in $D\geq4$ and for all bosonic spins

    hep-th 2026-07 conditional novelty 7.0

    Kerr-NUT mass/electric and equal-NUT/magnetic charges are dual in D≥4, realized as J_σ ↔ J_−σ in 3-point amplitudes generated by a spin-raising operator for all bosonic spins.

  2. Black Hole Interiors as a Laboratory for Time-Dependent Classical Double Copy

    hep-th 2026-04 unverdicted novelty 7.0

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

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    A single complex optical seed built from expansion and twist organizes stationary Kerr-Schild geometries, reconstructs the congruence, and encodes the zeroth-copy data that generates both the gravitational profile and...

  4. Minisuperspace Double Copy in Lifshitz Spacetimes

    hep-th 2026-04 unverdicted novelty 6.0

    A radial operator extracted from the reduced gravitational dynamics in Lifshitz spacetimes directly reproduces the Maxwell operator for the temporal single-copy field without using equations of motion.

  5. Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy

    hep-th 2026-04 unverdicted novelty 6.0

    The Kerr-Schild double copy enlarges residual symmetries at the ansatz level but preserves physical symmetries after cohomological reduction, exposing a mismatch between Yang-Mills and gravity residual symmetry structures.

  6. The Penrose Transform and the Kerr-Schild double copy

    hep-th 2025-11 unverdicted novelty 6.0

    The Kerr-Schild and twistorial double copies are equivalent for self-dual vacuum Kerr-Schild spacetimes.

  7. Residual Symmetries and Their Algebras in the Kerr-Schild Double Copy

    hep-th 2026-04 unverdicted novelty 5.0

    The Kerr-Schild double copy does not map residual symmetries between Yang-Mills and gravity; gravitational conformal Killing vectors are shown to be BRST-exact after a Weyl-compensated complex, leaving only global isometries.