Compactifying the Kerr-Schild Double Copy

TL;DR

This paper extends the classical double copy framework to Kaluza-Klein theories with gravity, gauge fields, and dilatons, using dimensional reduction of Kerr-Schild spacetimes to include black hole solutions in supergravity.

Contribution

It introduces a dimensionally reduced double copy for Kaluza-Klein theories and generalizes the boost-reduction method for generating charged black holes within Kerr-Schild spacetimes.

Findings

Identifies the single copy gauge and scalar fields for sKS solutions.

Shows the boost-reduction procedure applies to any stationary KS seed.

Proposes a double copy interpretation for multi-charge solutions.

Abstract

We show that the classical double copy relationship for Kerr-Schild spacetimes can be dimensionally reduced to give a natural notion of the double copy for Kaluza-Klein theory with gravity coupled to a gauge field and a dilaton. Under dimensional reduction the Kerr-Schild (KS) ansatz becomes the stringy Kerr-Schild (sKS) ansatz introduced by Wu. This ansatz captures many Kaluza-Klein black hole solutions, including single-charge black holes arising in both gauged and ungauged supergravity theories. We identify the single copy gauge field and scalar field of an arbitrary sKS solution. We show that the boost-reduction procedure for generating charged black hole solutions can be generalized to any stationary KS seed, and used to combine the metric with the zeroth and single copies of that seed into a single sKS solution. Furthermore, we comment on multi-charge solutions that can be written in a multi-sKS form, proposing a double copy interpretation involving multiple single copy sectors.