  Deep conceptual problems associated with classical black holes can be
addressed in string theory by the ``fuzzball'' paradigm, which provides a
microscopic description of a black hole in terms of a thermodynamically large
number of regular, horizonless, geometries with much less symmetry than the
corresponding black hole. Motivated by the tantalizing possibility to observe
quantum gravity signatures near astrophysical compact objects in this scenario,
we perform the first $3+1$ numerical simulations of a scalar field propagating
on a large class of multicenter geometries with no spatial isometries arising
from ${\cal N}=2$ four-dimensional supergravity. We identify the prompt
response to the perturbation and the ringdown modes associated with the photon
sphere, which are similar to the black-hole case, and the appearance of echoes
at later time, which is a smoking gun of some structure at the horizon scale
and of the regular interior of these solutions. The response is in agreement
with an analytical model based on geodesic motion in these complicated
geometries. Our results provide the first numerical evidence for the dynamical
linear stability of fuzzballs, and pave the way for an accurate discrimination
between fuzzballs and black holes using gravitational-wave spectroscopy.
