Superradiance is the wave analogue of the Penrose process whereby energy and angular momentum can be extracted from a black hole. In a confined background - for example AdS - the reflective asymptotic boundary conditions lead to an instability. The zero-modes of this instability signal a bifurcation to novel black holes that are not time independent neither axisymmetric. Instead they are time-periodic. Their single helical isometry evades the assumptions of Hawking's rigidity theorem, that would otherwise rule-out their existence. We construct these 'black resonators' within Einstein-AdS gravity, thus proving that Kerr-AdS is not the unique family of stationary solutions of the theory. In the zero horizon radius limit these resonators yield a 'geon', i.e. a time-periodic gravitational soliton that is a key player of the weakly turbulent nonlinear instability of AdS. From the properties of the black resonators we then argue and conjecture that the time evolution of the superradiant instability leads to a violation of the cosmic censorship.

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