Weak electromagnetic field admitting integrability in Kerr-NUT-(A)dS spacetimes

TL;DR

This paper identifies the most general weak electromagnetic field compatible with integrability in Kerr-NUT-(A)dS spacetimes, enabling exact solutions of particle and wave equations through separation of variables.

Contribution

It derives conditions for electromagnetic fields that preserve integrability and solves related equations explicitly in these complex spacetimes.

Findings

Most general compatible electromagnetic field found

Conditions for commutativity of observables established

Separation of variables achieved for Hamilton-Jacobi and Klein-Gordon equations

Abstract

We investigate properties of higher-dimensional generally rotating black-hole spacetimes, so called Kerr-NUT-(A)dS spacetimes, as well as a family of related spaces which share the same explicit and hidden symmetries. In these spaces, we study a particle motion in the presence of a weak electromagnetic field and compare it with its operator analogies. First, we find general commutativity conditions for classical observables and for their operator counterparts, then we investigate a fulfillment of these conditions in the Kerr-NUT-(A)dS and related spaces. We find the most general form of the weak electromagnetic field compatible with the complete integrability of the particle motion and the comutativity of the field operators. For such a field we solve the charged Hamilton-Jacobi and Klein-Gordon equations by separation of variables.