  Four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory, at a point
on the Coulomb branch where $SU(N)$ gauge symmetry is spontaneously broken to
$SU(N-1)\times U(1)$, admits BPS solitons describing a spherical shell of
electric and/or magnetic charges enclosing a region of unbroken gauge symmetry.
These solitons have been proposed as gauge theory models for certain features
of asymptotically flat extremal black holes. In the 't Hooft large $N$ limit
with large 't Hooft coupling, these solitons are holographically dual to
certain probe D3-branes in the $AdS_5 \times S^5$ solution of type IIB
supergravity. By studying linearised perturbations of these D3-branes, we show
that the solitons support quasinormal modes with a spectrum of frequencies
sharing both qualitative and quantitative features with asymptotically flat
extremal black holes.
