On the stability and deformability of top stars

TL;DR

This paper investigates the stability and deformability of top stars, horizonless solutions in higher-dimensional gravity, using various analytical and numerical techniques, and finds they are linearly stable with unique tidal response properties.

Contribution

It provides a comprehensive analysis of linear perturbations, stability, and tidal responses of top stars, introducing new insights into their quasi-normal modes and dynamical Love numbers.

Findings

All mode frequencies have negative imaginary parts indicating stability.

Top stars exhibit zero static Love numbers but non-trivial dynamical Love numbers.

Identified three classes of quasi-normal modes: prompt, long-lived, and 'blind' modes.

Abstract

Topological stars, or top stars for brevity, are smooth horizonless static solutions of Einstein-Maxwell theory in 5-d that reduce to spherically symmetric solutions of Einstein-Maxwell-Dilaton theory in 4-d. We study linear scalar perturbations of top stars and argue for their stability and deformability. We tackle the problem with different techniques including WKB approximation, numerical analysis, Breit-Wigner resonance method and quantum Seiberg-Witten curves. We identify three classes of quasi-normal modes corresponding to prompt-ring down modes, long-lived meta-stable modes and what we dub `blind' modes. All mode frequencies we find have negative imaginary parts, thus suggesting linear stability of top stars. Moreover we determine the tidal Love and dissipation numbers encoding the response to tidal deformations and, similarly to black holes, we find zero value in the static limit but, contrary to black holes, we find non-trivial dynamical Love numbers and vanishing dissipative effects at linear order. For the sake of illustration in a simpler context, we also consider a toy model with a piece-wise constant potential and a centrifugal barrier that captures most of the above features in a qualitative fashion.