Stability ranges of magnetic black holes and mirror (topological) stars in 5D gravity

TL;DR

This paper analyzes the stability of magnetic black holes and mirror stars in 5D gravity, identifying parameter ranges for stability and calculating their perturbation frequencies, challenging previous stability claims.

Contribution

It provides a detailed stability analysis of 5D magnetic black holes and mirror stars, including new stability boundaries and perturbation frequency calculations.

Findings

Mirror stars are stable only when their radius is below approximately 4.004 times their mass.

Black holes are stable across the entire parameter space studied.

The stability results contradict some earlier findings in the literature.

Abstract

We discuss static, spherically symmetric solutions to the 5D Einstein-Maxwell equations (belonging to wide classes of multidimensional solutions known at least from the 1990s) and select among them those which must observationally look like local objects whose surface reflects back particles or signals getting there, the so-called mirror stars (also called ``topological stars'' by some authors). Their significant parameters are the Schwarzschild mass $m$ and the magnetic charge $q$, such that $q^2 > 3m^2$, while the radius of their mirror surface is $r_b = 2q^2/(3m) > 2m$. We also discuss their black hole counterparts for which $q^2 \leq 3m^2$. For both these objects, we study spherically symmetric time-dependent perturbations and determine the stability regions in their parameter spaces. Thus, mirror stars turn out to be stable only at $r_b < r_b^{\rm crit} \approx 4.004\,m$, while the black holes prove to be stable in the whole range of their parameters. We calculate the fundamental frequencies and decay rates of black hole perturbations using the WKB and time domain methods. Our stability results disagree with some of those previously announced in the literature.