Charged particle in higher dimensional weakly charged rotating black hole spacetime

TL;DR

This paper investigates the motion of charged particles around weakly charged higher-dimensional rotating black holes, demonstrating integrability and separability of equations of motion under specific electromagnetic configurations.

Contribution

It introduces a specific electromagnetic field configuration proportional to a primary Killing vector that renders the equations of motion integrable in higher-dimensional Kerr-NUT-(A)dS spacetimes.

Findings

Equations of motion are completely integrable for certain electromagnetic fields.

Hamilton-Jacobi and Klein-Gordon equations are separable in this setting.

A full set of conserved quantities in involution is identified.

Abstract

We study charged particle motion in weakly charged higher dimensional black holes. To describe the electromagnetic field we use a test field approximation and use the higher dimensional Kerr-NUT-(A)dS metric as a background geometry. It is shown that for a special configuration of the electromagnetic field the equations of motion of charged particles are completely integrable. The vector potential of such a field is proportional to one of the Killing vectors (called primary Killing vector) from the `Killing tower' of symmetry generating objects which exists in the background geometry. A free constant in the definition of the adopted electromagnetic potential is proportional to the electric charge of the higher dimensional black hole. The full set of independent conserved quantities in involution is found. It is demonstrated, that Hamilton-Jacobi equations are separable, as well as the corresponding Klein-Gordon equation and its symmetry operators.