The Newman-Penrose Map and the Classical Double Copy

TL;DR

This paper introduces the Newman-Penrose map, a new classical double copy relating certain Einstein solutions to Maxwell solutions, enabling exploration of gravity solutions beyond vacuum and stationary cases.

Contribution

The paper presents the first systematic classical double copy map applicable to non-vacuum, non-stationary spacetimes, expanding the scope of gauge-gravity duality in classical solutions.

Findings

Mapped Schwarzschild and Kerr black holes to Maxwell solutions.

Extended the double copy framework to non-vacuum, non-stationary spacetimes.

Provided a systematic approach for exploring new gravity solutions.

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.