Vortex String Formation in Black Hole Superradiance of a Dark Photon with the Higgs Mechanism

Black hole superradiance, which only relies on gravitational interactions, can provide a powerful probe of the existence of ultralight bosons that are weakly coupled to ordinary matter. However, as a boson cloud grows through superradiance, nonlinear effects from interactions with itself or other fields may become important. As a representative example of this, we use nonlinear evolutions to study black hole superradiance of a vector boson that attains a mass, via a coupling to a complex scalar, through the Higgs mechanism. For the cases considered, we find that the superradiant instability can lead to a transient period where the scalar field reaches its symmetry restoration value, leading to the formation of closed vortex strings, the temporary disruption of the exponential growth of the cloud, and an explosive outburst of energy. After the cloud loses sufficient mass, the superradiant growth resumes, and the cycle repeats. Thus, the black hole will be spun down but, potentially, at a much lower rate compared to when nonlinear effects are unimportant and with the liberated energy going primarily into bosonic radiation instead of gravitational waves.