Charge (in)stability and superradiance of Topological Stars

TL;DR

This paper investigates the stability and superradiance of Topological Stars under charged scalar perturbations, finding they are linearly stable and analyzing charge amplification in Black Strings.

Contribution

It introduces a comprehensive analysis of perturbations and superradiance in Topological Stars and Black Strings using multiple advanced techniques, including Seiberg-Witten theory.

Findings

All mode frequencies decay exponentially, indicating linear stability.

Charge superradiance is characterized and quantified.

Multiple methods confirm the stability results.

Abstract

We study linear massive scalar charged perturbations of Topological Stars in the fuzzball and in the black hole (Black String) regimes. The objects that naturally couple to the electric 3-form field strength of these solutions are charged strings, wound around the compact direction. We explore the possibility of instabilities of these solutions, in analogy with the charge instability already highlighted for other non-BPS geometries like JMaRT. This issue is addressed by calculating quasi-normal mode frequencies with a variety of techniques: WKB approximation, direct integration, Leaver method and by exploiting the recently discovered correspondence between black hole-fuzzball perturbation theory and quantum Seiberg-Witten curves. All mode frequencies we find have negative imaginary parts, implying an exponential decay in time. This suggests a linear stability of Topological Stars also in this new scenario. In addition, we study the charge superradiance for the Black String. We compute the amplification factor with the numerical integration method and a quantum Seiberg-Witten motivated definition including instantonic corrections.