Double Kerr-Schild spacetimes and the Newman-Penrose map

TL;DR

This paper extends the Newman-Penrose map to a wider class of spacetimes, linking exact Einstein solutions to self-dual gauge fields, and demonstrates this with the Kerr-Taub-NUT-(A)dS spacetime, revealing a novel electric-magnetic duality.

Contribution

It introduces an extension of the Newman-Penrose map to more general spacetimes and connects it with classical double copy constructions.

Findings

The extended map successfully associates self-dual gauge fields to new spacetime classes.

The resulting gauge fields exhibit a unique electric-magnetic duality.

The approach aligns with previously known double copy examples.

Abstract

The Newman-Penrose map, which is closely related to the classical double copy, associates certain exact solutions of Einstein's equations with self-dual solutions of the vacuum Maxwell equations. Here we initiate an extension of the Newman-Penrose map to a broader class of spacetimes. As an example, we apply principles from the Newman-Penrose map to associate a self-dual gauge field to the Kerr-Taub-NUT-(A)dS spacetime and we show that the result agrees with previously studied examples of classical double copies. The corresponding field strength exhibits a discrete electric-magnetic duality that is distinct from its (Hodge star) self-dual property.