Tests for the existence of horizon through gravitational waves from a small binary in the vicinity of a massive object

In this letter we calculate the gravitational waves (GWs) emitted from a small binary (SB) by solving the Teukolsky equation in the background of a massive exotic compact object (ECO) which is phenomenologically described by a Schwarzschild geometry with a reflective boundary condition at its ``would-be'' horizon. The ``continuous echo" waves propagating to infinity due to reflectivity of ECO at its ``would-be'' horizon provide an exquisite probe to the nature of the ECO's horizon.