Black hole accretion of scalar clouds with spontaneous symmetry breaking

Spontaneous scalarization of black holes typically occurs through the condensation of a scalar field, with the field evolving from a $U(1)$-symmetric phase into a symmetry-breaking one with lower energy. We show that there exist symmetry-breaking phases which are themselves unstable to the formation of an additional scalar condensate, or `cloud', which is partly accreted into the black hole. By studying the fully nonlinear dynamical evolution of the process, we find that symmetry breaking causes the accretion channels of scalar clouds to be non-degenerate, favoring a dominant channel for evolution. Additionally, the final states form a characteristic energy band due to varying amounts of radiation emitted by clouds in different channels.