Universality in quasinormal modes of a magnetized black hole

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.