Universality in quasinormal modes of a magnetized black hole

TL;DR

This paper studies linear charged-scalar perturbations of the Ernst–Schwarzschild black hole in a uniform magnetic field, using frequency- and time-domain analyses. It reveals a universal scaling of the quasinormal mode spectrum near a critical charge $q_c = mB$, with a real-frequency exponent $\gamma \approx \tfrac{1}{2}$ and vanishing damping at criticality, interpreted as a confinement–deconfinement transition with a scale $\sim 1/B$. The results show mode-coupling effects lead to long-lived, near-degenerate modes and emergent spectral features, suggesting a robust universal behavior that could inform more realistic magnetized compact-object models. While framed in the non-asymptotically flat Ernst spacetime, the work highlights how magnetic fields imprint qualitative and quantitative changes on wave dynamics around black holes, potentially guiding future investigations with rotation and backreaction.

Abstract

Black holes (BHs) in magnetized environments are a topic of intense research, both theoretical and observational. In particular, the interaction between charged matter and such objects provides a rich arena with applications ranging from fundamental field theory to high-energy astrophysics. In this work, we investigate the linear stability of a magnetized Einstein-Maxwell solution describing a static, axially symmetric BH immersed in a uniform magnetic field. 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.

Figures (4)

• Figure 1: Effective potential for different values of the perturbation charge $q$. We set $BM=0.02$, $\ell=m=1$, and $\mu=0$. Note that the growth at the critical charge $q_c$ (red dashed) is weaker.
• Figure 2: Quasi-normal spectrum of a massless perturbation as a function of the charge field normalized to the critical charge, $q_c$. The chosen parameters are $MB=0.1$ with $\ell=m=1$. We observe two distinct regimes, separated by the effective critical charge $Q_c$.
• Figure 3: Time-domain profiles (top: decoupled; bottom: coupled with $\ell_{\max}=5$) for $m=1$, and $BM=0.1$. Left: $\ell=1,2$, $q/q_c=0.5$; right: $\ell=1$, $q/q_c =1.08$. The decay rate decreases not only with increasing multipole number, but also as the critical charge is approached.
• Figure 4: Fourier spectrum for the simulations shown in Fig. \ref{['TimeDomain']} for $\ell=1$. Far from the critical charge, we observe only the fundamental mode (top left). However, as we approach $q_c$, additional modes are excited, producing an echo-like profile (top right). When we take the coupling into account (bottom panels), we observe echoes even far from the critical charge (left), as well as an increase in the number of excited frequencies near the critical charge (right). Moreover, close to the critical charge we find that the lowest-lying modes have an extremely small imaginary part in the decoupled case, and an even smaller one in the coupled case.