Why is the Weyl double copy local in position space?

Abstract

The double copy relates momentum-space scattering amplitudes in gauge and gravity theories. It has also been extended to classical solutions, where in some cases an exact double copy can be formulated directly in terms of products of fields in position space. This is seemingly at odds with the momentum-space origins of the double copy, and the question of why exact double copies are possible in position space and when this form will break has remained largely unanswered. In this paper, we provide an answer to this question, using a recently developed twistorial formulation of the double copy. We show that for certain vacuum type-D solutions, the momentum-space, twistor-space and position-space double copies amount to the same thing, and are directly related by integral transforms. Locality in position space is ultimately a consequence of the very special form of momentum-space three-point amplitudes, and we thus confirm suspicions that local position-space double copies are possible only for highly algebraically-special spacetimes.

23 pages plus references, 5 figures

References in corpus (12)

• Black holes and the double copy
• The Kerr-Schild double copy in curved spacetime
• Yang-Mills origin of gravitational symmetries
• A Twistorial Foundation for the Classical Double Copy
• Strings, extended objects, and the classical double copy
• Unfolded Description of $Ad{S}_4$ Kerr Black Hole
• Alternative formulations of the twistor double copy
• Black Holes in Klein Space
• Anti-Self-Dual Spacetimes, Gravitational Instantons and Knotted Zeros of the Weyl Tensor
• The Weyl double copy in vacuum spacetimes with a cosmological constant
• Weyl double copy and massless free fields in curved spacetimes
• BRST Symmetry and the Convolutional Double Copy

Cited by in corpus (14)

• Einstein-Maxwell theory and the Weyl double copy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Black Hole Horizons from the Double Copy
• Double Copy from Tensor Products of Metric BV${}^{■}$-algebras
• Regularized Weyl double copy
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• Asymptotic Weyl double copy in Newman-Penrose formalism
• Compactifying the Kerr-Schild Double Copy
• Gravito-electromagnetism, Kerr-Schild and Weyl double copies; a unified perspective
• Weyl double copy in type D spacetime in four and five dimensions
• Background ambiguity and the Gödel double copy
• Hawking radiation from the double copy
• New framework for classical double copies
• Five dimensional Weyl double copy