Twistor Space Origins of the Newman-Penrose Map

Abstract

Recently, we introduced the "Newman-Penrose map," a novel correspondence between a certain class of solutions of Einstein's equations and self-dual solutions of the vacuum Maxwell equations, which we showed was closely related to the classical double copy. Here, we give an alternative definition of this correspondence in terms of quantities that are defined naturally on twistor space, and a shear-free null geodesic congruence on Minkowski space whose twistorial character is articulated by the Kerr theorem. The advantage of this reformulation is that it is purely geometrical in nature, being manifestly invariant under both spacetime diffeomorphisms and projective transformations on twistor space. While the original formulation of the map may be more convenient for most explicit calculations, the twistorial formulation we present here may be of greater theoretical utility.

13 pages, v2: references and some clarifications added, results unchanged, v3: further clarifications and one figure added

References in corpus (11)

• New Relations for Gauge-Theory Amplitudes
• Black holes and the double copy
• The Kinematic Algebra From the Self-Dual Sector
• The Kerr-Schild double copy in curved spacetime
• Scattering on plane waves and the double copy
• A Twistorial Foundation for the Classical Double Copy
• The Classical Double Copy of a Point Charge
• A double copy for asymptotic symmetries in the self-dual sector
• Heterotic Kerr-Schild Double Field Theory and Classical Double Copy
• The Weyl double copy from twistor space
• Some geometry of de Sitter space

Cited by in corpus (19)

• Classical double copy at null infinity
• Asymptotic Weyl Double Copy
• Kerr-Schild Double Copy of the Coulomb Solution in Three Dimensions
• Einstein-Maxwell theory and the Weyl double copy
• The Off-Shell Recursion for Gravity and the Classical Double Copy for currents
• Alternative formulations of the twistor double copy
• The double copy of the multipole expansion
• Why is the Weyl double copy local in position space?
• Isometries and the double copy
• Non-perturbative aspects of the self-dual double copy
• The single copy of the gravitational holonomy
• Aligned Fields Double Copy to Kerr-NUT-(A)dS
• Radiative phase space extensions at all orders in r for self-dual Yang-Mills and Gravity
• A spinorial double copy for $\mathcal{N}=0$ supergravity
• The double copy: from optics to quantum gravity
• Weyl-Lewis-Papapetrou coordinates, self-dual Yang-Mills equations and the single copy
• Background ambiguity and the Gödel double copy
• Massive Covariant Colour-Kinematics in 3D
• Untwisting the double copy: the zeroth copy as an optical seed