  We study scalar perturbations of topological solitons, smooth horizonless
solutions in five-dimensional Einstein-Maxwell theory that correspond to
coherent states of gravity via the dynamics of extra compact dimensions. First,
we compute scalar quasinormal modes for topological stars that have a single
unstable photon sphere, and we show that the spectrum is very similar to that
of a black hole with the same photon sphere. Next, we study topological stars
that have both a stable inner photon sphere and an unstable one. The first few
quasinormal modes are localized around the inner photon sphere. The spectrum
also contains ''black-hole like modes'' localized at the unstable outer photon
sphere. The frequencies of these modes are similar to those of a black hole,
but their imaginary part is smaller due to a cavity effect associated with the
inner photon sphere. The longer damping produced by this trapping effect may
have implications for black hole spectroscopy.
