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Exotic compact objects (ECOs) have recently become an exciting researchsubject, since they are speculated to have a special response to the incidentgravitational waves (GWs) that leads to GW echoes. We show that energy carriedby GWs can easily cause the event horizon to form out of a static ECO ---leaving no echo signals towards spatial infinity. To show this, we use theingoing Vaidya spacetime and take into account the back reaction due toincoming GWs. Demanding that an ECO does not collapse into a black hole puts anupper bound on the compactness of the ECO, at the cost of less distinct echosignals for smaller compactness. The trade-off between echoes' detectabilityand distinguishability leads to a fine tuning of ECO parameters for LIGO tofind distinct echoes. We also show that an extremely compact ECO that cansurvive the gravitational collapse and give rise to GW echoes might have toexpand its surface in a non-causal way.

Instability of exotic compact objects and its implications for gravitational-wave echoes