Non-linear Q -clouds around Kerr black holes

Q -balls are regular extended 'objects' that exist for some non-gravitating, self-interacting, scalar field theories with a global, continuous, internal symmetry, on Minkowski spacetime. Here, analogous objects are also shown to exist around rotating (Kerr) black holes, as non-linear bound states of a test scalar field. We dub such configurations Q -clouds. We focus on a complex massive scalar field with quartic plus hexic self-interactions. Without the self-interactions, linear clouds have been shown to exist, in synchronous rotation with the black hole horizon, along 1-dimensional subspaces - existence lines -of the Kerr 2-dimensional parameter space. They are zero modes of the superradiant instability. Non-linear Q -clouds, on the other hand, are also in synchronous rotation with the black hole horizon; but they exist on a 2-dimensional subspace, delimited by a minimal horizon angular velocity and by an appropriate existence line, wherein the non-linear terms become irrelevant and the Q -cloud reduces to a linear cloud. Thus, Q -clouds provide an example of scalar bound states around Kerr black holes which, generically, are not zero modes of the superradiant instability. We describe some physical properties of Q -clouds, whose backreaction leads to a new family of hairy black holes, continuously connected to the Kerr family. (C) 2014 The Authors. Published by Elsevier B.V.