The Penrose Transform and the Kerr-Schild double copy

TL;DR

This paper demonstrates the equivalence of two classical double copy prescriptions for a broad class of self-dual vacuum solutions in Kerr-Schild spacetimes, using twistor theory and null Lorentz transformations.

Contribution

It establishes the equivalence of Kerr-Schild and twistorial double copies for twistorial Kerr-Schild spacetimes, with explicit illustration for the self-dual Kerr-Taub-NUT spacetime.

Findings

Proves the equivalence of two double copy prescriptions for a class of solutions.

Uses null Lorentz transformations and twistor functions in the proof.

Explicitly demonstrates the equivalence for the self-dual Kerr-Taub-NUT spacetime.

Abstract

There are a number of classical double copies, each providing a prescription for generating solutions to the Maxwell and scalar wave equations from exact solutions of Einstein's equations. Two such prescriptions are the Kerr-Schild and twistorial double copies. We argue that for a broad class of self-dual vacuum solutions of the Kerr-Schild form, which we refer to as twistorial Kerr-Schild spacetimes, these two prescriptions are in fact equivalent. The approach is elementary, utilizing null Lorentz transformations, with homogenous functions on twistor space playing a central role. The equivalence is illustrated explicitly for the example of the self-dual (Kerr)-Taub-NUT spacetime. A detailed proof and several more examples will be presented in a long-form companion to this letter.