  The merger of colliding black holes (BHs) should lead to the production of
ringdown or quasinormal modes (QNMs), which may very well be sensitive to the
state of the interior. We put this idea to the test with a recent proposal that
the interior of a BH consists of a bound state of highly excited, long, closed,
interacting strings; figuratively, a collapsed polymer. We show that such BHs
do indeed have a distinct signature in their QNM spectrum: A new class of modes
whose frequencies are parametrically lower than the lowest-frequency mode of a
classical BH and whose damping times are parametrically longer. The reason for
the appearance of the new modes is that our model contains another scale, the
string length, which is parametrically larger than the Planck length. This
distinction between the collapsed-polymer model and general-relativistic BHs
could be made with gravitational-wave observations and offers a means for
potentially measuring the strength of the coupling in string theory. For
example, GW150914 already allows us to probe the strength of the string
coupling near the regime which is predicted by the unification of the
gravitational and gauge-theory couplings. We also derive bounds on the
amplitude of the collapsed-polymer QNMs that can be placed by current and
future gravitational-wave observations.
