Aligned fields double copy to Kerr-NUT-(A)dS

We show that the Killing tensor of the Kerr spacetime has an analogue in the $$ \sqrt{\textrm{Kerr}} $$ Kerr gauge theory solution related to it by the classical double copy. This hidden symmetry of $$ \sqrt{\textrm{Kerr}} $$ Kerr leads to an additional constant of motion for color-charged point particles moving in it, implying integrability of the equation of motion. These are the gauge theory counterparts to the Carter constant and the integrability of the geodesic equation in a Kerr background.

Section: Jhep10(2023)085 6 Discussionsupporting

confidence: 84%

Hidden symmetry in the double copy

Ball,

Bencke,

Chen

et al. 2023

“…Similarly, the Taub-NUT spacetime in four dimensions can be written in double Kerr-Schild form, and in D dimensions it can analogously be written in a multi-Kerr-Schild form with D/2 mutually orthogonal null geodesics [43]. This multi-Kerr-Schild coordinate system enables a double copy interpretation of these metrics in four and higher dimensions [11,44]. The connection between these results and the generalization of the sKS ansatz to include NUT charge is worthy of further study.…”

Section: Jhep05(2023)198mentioning

confidence: 99%

Compactifying the Kerr-Schild double copy

Dempsey

Weck

2023

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.

A spinorial double copy for $$ \mathcal{N} $$ = 0 supergravity

Armstrong-Williams

White

2023

The Weyl double copy is a formula relating solutions of scalar, gauge and gravity theories, and is related to the BCJ double copy for scattering amplitudes. The latter relates Yang-Mills theory to $$ \mathcal{N} $$ N = 0 supergravity, where an axion and dilaton are present in addition to the graviton. However, the traditional Weyl double copy applies only to pure gravity solutions, such that it remains to be seen whether or not it can be extended to the full spectrum of $$ \mathcal{N} $$ N = 0 supergravity. We examine this question using recently developed twistor methods, showing that some sort of double copy formula for $$ \mathcal{N} $$ N = 0 supergravity is indeed possible for certain solutions. However, it differs both from the traditional Weyl double copy form, and recent conjectures aimed at generalising the Weyl double copy to non-vacuum solutions.