Ringdown signatures in the Ernst-Wild geometry: modeling Kerr black holes immersed in a magnetic field

We analyze the quasinormal mode spectrum for Kerr black holes surrounded by an asymptotically uniform magnetic field, modeled with the Ernst-Wild geometry. A perturbative expansion in both the rotation parameter $a$ and the magnetic field $B$ allows the analysis of perturbations with Kerr-like asymptotics well inside the Melvin radius, and we obtain the spectrum for a variety of scalar quasinormal modes over a range of parameters using the continued fraction method. We then interpolate the low-lying mode spectrum to construct an Ernst-Wild template for the ringdown, and use the LIGO-Virgo-KAGRA analysis tool pyRing to assess the impact of the magnetosphere on the extraction of ringdown signatures from several observed binary black hole mergers.