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We present numerical waveforms of gravitational-wave echoes from spinningexotic compact objects (ECOs) that result from binary black hole coalescence.We obtain these echoes by solving the Teukolsky equation for the $\psi_4$associated with gravitational waves that propagate toward the horizon of a Kerrspacetime, and process the subsequent reflections of the horizon-going wave bythe surface of the ECO, which lies right above the Kerr horizon. Thetrajectories of the infalling objects are modified from Kerr geodesics, suchthat the gravitational waves propagating toward future null infinity matchthose from merging black holes with comparable masses. In this way, thecorresponding echoes approximate to those from comparable-mass mergers. Forboundary conditions at the ECO surface, we adopt recent work using the membraneparadigm, which relates $\psi_0$ associated with the horizon-going wave and$\psi_4$ of the wave that leaves the ECO surface. We obtain $\psi_0$ of thehorizon-going wave from $\psi_4$ using the Teukolsky-Starobinsky relation. Theechoes we obtain turn out to be significantly weaker than those from previousstudies that generate echo waveforms by modeling the ringdown part of binaryblack hole coalescence waveforms as originating from the past horizon.

Gravitational-wave echoes from spinning exotic compact objects: numerical waveforms from the Teukolsky equation