  While recent detections of gravitational waves from the mergers of binary
black holes match well with the predictions of General Relativity (GR), they
cannot directly confirm the existence of event horizons. Exotic compact objects
(ECOs) are motivated by quantum models of black holes, and can have exotic
structure (or a "wall") just outside the (would-be) horizon. ECOs produce
similar ringdown waveforms to the GR black holes, but they are followed by
delayed "echoes". By solving linearized Einstein equations we can model these
echoes and provide analytic templates that can be used to compare to
observations. For concreteness, we consider GW150914 event, detected by the
LIGO/Virgo collaboration, and study the model dependence of its echo
properties. We find that echoes are reasonably approximated by complex
gaussians, with amplitudes that decay as a power law in time, while their width
in time (frequency) grows (shrinks) over subsequent echoes. We also show that
trapped modes between a perfectly reflecting wall and angular momentum barrier
in Kerr metric can exhibit superradiant instability over long times, as
expected.
