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Within Einstein's theory of gravity, any compact object heavier than a fewsolar masses must be a black hole. Any observation showing otherwise wouldimply either new physics beyond General Relativity or new exotic matter fieldsbeyond the Standard Model, and might provide a portal to understand somepuzzling properties of a black hole. We give a short overview on tests of thenature of dark compact objects with present and future gravitational-waveobservations, including inspiral tests of the multipolar structure of compactobjects and of their tidal deformability, ringdown tests, and searches fornear-horizon structures with gravitational-wave echoes.

Testing the nature of dark compact objects with gravitational waves