A Note on Particles and Scalar Fields in Higher Dimensional Nutty Spacetimes

TL;DR

This paper investigates the integrability and separability of geodesic and scalar field equations in a broad class of higher-dimensional NUT-charged spacetimes, revealing the role of Killing tensors in these processes.

Contribution

It introduces a general framework for analyzing geodesic and scalar field equations in complex higher-dimensional NUT spacetimes, highlighting the existence of Killing tensors that enable separability.

Findings

Geodesic equations are integrable due to non-trivial Killing tensors.

Klein-Gordon equation is completely separable in these backgrounds.

The study encompasses a wide class of solutions including charged and cosmological constant cases.

Abstract

In this note, we study the integrability of geodesic flow in the background of a very general class of spacetimes with NUT-charge(s) in higher dimensions. This broad set encompasses multiply NUT-charged solutions, electrically and magnetically charged solutions, solutions with a cosmological constant, and time dependant bubble-like solutions. We also derive first-order equations of motion for particles in these backgrounds. Separability turns out to be possible due to the existence of non-trivial irreducible Killing tensors. Finally, we also examine the Klein-Gordon equation for a scalar field in these spacetimes and demonstrate complete separability.