Universality in quasinormal modes of a magnetized black hole

TL;DR

This paper studies the stability and quasinormal modes of a magnetized black hole, revealing a universal power-law scaling at a critical charge that distinguishes confined and deconfined wave regimes.

Contribution

It introduces a detailed analysis of QNM behavior in magnetized black holes, identifying a universal scaling law at a critical charge value.

Findings

Identified a critical charge where QNM spectrum shows power-law scaling with exponent ~1/2.

Discovered a transition between confined and deconfined wave regimes based on magnetic field influence.

Provided insights into wave trapping and damping in strongly magnetized black hole environments.

Abstract

In this work, we investigate the linear stability of a magnetized Einstein-Maxwell solution describing a static, axially symmetric black hole (BH) immersed in a uniform magnetic field $B$. We probe the dynamics of an external charged scalar field through its quasinormal modes (QNMs), combining frequency- and time-domain analyses. We find a critical value of the field charge at which the QNM spectrum exhibits universal power-law scaling with an exponent of approximately $1/2$. This critical behavior admits a simple interpretation in terms of a transition between a confined regime, where waves remain effectively trapped within a region of characteristic size $\sim 1/B$, and a deconfined regime, where the field reaches distances $\gg 1/B$ and the damping rate becomes parametrically small. These results provide qualitative and quantitative insights that may inform more realistic scenarios involving highly magnetized compact objects.