Non-spinning tops are stable

TL;DR

This paper analyzes the stability of five-dimensional Einstein-Maxwell solutions, finding that non-spinning topological stars and black strings are generally stable, with certain perturbations potentially causing instabilities.

Contribution

It provides a detailed quasinormal mode analysis of coupled gravitational and electromagnetic perturbations in these solutions, demonstrating classical stability in specific parameter ranges.

Findings

Odd perturbations decay over time.

Spherical symmetric even perturbations can be unstable under certain conditions.

Topological stars and black strings are classically stable within a finite parameter space.

Abstract

We consider coupled gravitational and electromagnetic perturbations of a family of five-dimensional Einstein-Maxwell solutions that describes both magnetized black strings and horizonless topological stars. We find that the odd perturbations of this background lead to a master equation with five Fuchsian singularities and compute its quasinormal mode spectrum using three independent methods: Leaver, WKB and numerical integration. Our analysis confirms that odd perturbations always decay in time, while spherically symmetric even perturbations may exhibit for certain ranges of the magnetic fluxes instabilities of Gregory-Laflamme type for black strings and of Gross-Perry-Yaffe type for topological stars. This constitutes evidence that topological stars and black strings are classically stable in a finite domain of their parameter space.