Hidden Symmetry in the Double Copy

TL;DR

This paper reveals a hidden symmetry in the gauge theory counterpart of the Kerr spacetime, leading to integrability of color-charged particle motion and extending the classical double copy concept.

Contribution

It demonstrates the existence of a Kerr-like hidden symmetry in the gauge theory solution related by the double copy, introducing new integrability properties.

Findings

Identification of a gauge theory analogue of the Kerr Killing tensor.

Discovery of an additional constant of motion for color-charged particles.

Implication of integrability in gauge theory dynamics similar to Kerr spacetime.

Abstract

We show that the Killing tensor of the Kerr spacetime has an analogue in the $\sqrt{\rm Kerr}$ gauge theory solution related to it by the classical double copy. This hidden symmetry of $\sqrt{\rm Kerr}$ 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.