Nonlinear photon-plasma interaction and the black hole superradiant instability

Electromagnetic field confinement due to plasma near accreting black holes can trigger superradiant instabilities at the linear level, limiting the spin of black holes and providing novel astrophysical sources of electromagnetic bursts. However, nonlinear effects might jeopardize the efficiency of the confinement, rending superradiance ineffective. Motivated by understanding nonlinear interactions in this scenario, here we study the full $3+1$ nonlinear dynamics of Maxwell equations in the presence of plasma by focusing on regimes that are seldom explored in standard plasma-physics applications, namely a generic electromagnetic wave of very large amplitude but small frequency propagating in an inhomogeneous, overdense plasma. We show that the plasma transparency effect predicted in certain specific scenarios is not the only possible outcome in the nonlinear regime: plasma blow-out due to nonlinear momentum transfer is generically present and allows for significant energy leakage of electromagnetic fields above a certain threshold. We argue that such effect is sufficient to dramatically quench the plasma-driven superradiant instability around black holes even in the most optimistic scenarios.