The Newman-Penrose Map and the Classical Double Copy

Abstract

Gauge-gravity duality is arguably our best hope for understanding quantum gravity. Considerable progress has been made in relating scattering amplitudes in certain gravity theories to those in gauge theories---a correspondence dubbed the "double copy". Recently, double copies have also been realized in a classical setting, as maps between exact solutions of gauge theories and gravity. We present here a novel map between a certain class of real, exact solutions of Einstein's equations and self-dual solutions of the flat-space vacuum Maxwell equations. This map, which we call the "Newman-Penrose map", is well-defined even for non-vacuum, non-stationary spacetimes, providing a systematic framework for exploring gravity solutions in the context of the double copy that have not been previously studied in this setting. To illustrate this, we present here the Newman-Penrose map for the Schwarzschild and Kerr black holes, and Kinnersley's photon rocket.

arXiv comment37 pages, 2 figures, v2: 39 pages, 2 figures, typos fixed, references added

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Cited by in corpus (37)

• A Twistorial Foundation for the Classical Double Copy
• The Weyl Double Copy for Gravitational Waves
• Classical Solutions and their Double Copy in Split Signature
• A double copy for asymptotic symmetries in the self-dual sector
• Off-Shell Color-Kinematics Duality for Chern-Simons
• Classical double copy at null infinity
• New heavenly double copies
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• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Alternative formulations of the twistor double copy
• Twistor Space Origins of the Newman-Penrose Map
• The double copy of the multipole expansion
• Why is the Weyl double copy local in position space?
• Geodesics From Classical Double Copy
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• Isometries and the double copy
• The Classical Double Copy for M-theory from a Kerr-Schild Ansatz for Exceptional Field Theory
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• Weyl double copy and massless free fields in curved spacetimes
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• Generalized Black Holes in 3D Kerr-Schild Double Copy
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• Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy
• Background ambiguity and the Gödel double copy
• Next-to-MHV Yang-Mills kinematic algebra
• The Weyl double copy from twistor space
• Untwisting the double copy: the zeroth copy as an optical seed
• The Kerr-Schild Double Copy in Lifshitz Spacetime
• NS-NS Spacetimes from Amplitudes
• Cotton Double Copy for Gravitational Waves