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Most of the properties of black holes can be mimicked by horizonless compact objects such as gravastars, boson stars, wormholes and superspinars. These "black hole mimickers" develop a strong ergoregion instability when rapidly spinning. Instability timescales can be of the order of 0.1 seconds to 1 week for objects with mass M = 1-10^6 M_{sun} and angular momentum J > 0.4M^2 . This provides a strong indication that very compact objects with large rotation are black holes.