Quasinormal modes for subtracted rotating and magnetized geometries

We obtain explicit separable solutions of the wave equation of massless minimally coupled scalar fields in the subtracted geometry of four-dimensional rotating and Melvin (magnetised) four-charge black holes of the STU model, a consistent truncation of maximally supersymmetric supergravity with four types of electromagnetic fields. These backgrounds possess a hidden $\mathrm{SL}(2,\mathrm{R})\times \mathrm{SL}(2,\mathrm{R})\times \mathrm{SO}(3)$ symmetry and faithfully model the near-horizon geometry of these black holes, but locate them in a confining asymptotically conical box. For each subtracted geometry we obtain two branches of quasinormal modes, given in terms of hypergeometric functions and spherical harmonics. One branch is over-damped and the other under-damped and they exhibit rotational splitting. No black hole bomb is possible because the Killing field which corotates with the horizon is everywhere timelike outside the black hole. A five-dimensional lift of these geometries is given locally by the product of a Bañados-Teitelboim-Zanelli black hole with a two-sphere. This allows an explicit analysis of the minimally coupled massive five-dimensional scalar field. Again, there are two branches, both damped; however, now their oscillatory parts are shifted by the quantized wave number $k$ along the fifth circle direction.