Stable Magnetic Universes Revisited

TL;DR

This paper revisits static magnetic universe solutions across all dimensions, analyzing their stability and particle geodesics, revealing dimension-dependent stability properties and particle confinement behaviors.

Contribution

It rederives magnetic universe metrics in a new form, providing a comprehensive stability analysis across dimensions and exploring particle trajectories.

Findings

Spacetimes are stable for dimensions d>3 at all radii.

For d=3, stability cannot be maintained simultaneously near and far from the center.

Neutral particles are confined near the center, while charged particles in d=4 escape to infinity.

Abstract

A regular class of static, cylindrically symmetric pure magnetic field metrics is rederived in a different metric ansatz in all dimensions. Radial, time dependent perturbations show that for dimensions d>3 such spacetimes are stable at both near r\approx0 and large radius r\rightarrow\infty. In a different gauge these stability analysis and similar results were known beforehand. For d=3, however, simultaneous stability requirement at both, near and far radial distances can not be reconciled for time - dependent perturbations. Restricted, numerical geodesics for neutral particles reveal a confinement around the center in the polar plane. Charged, time-like geodesics for d=4 on the other hand are shown numerically to run toward infinity.