Do fermions condense and freeze at a black hole's edge?

Near a black hole's event horizon, the usual quantum rules governing fermions — particles that normally refuse to share the same state — may need revision due to extreme spacetime curvature. Injecting a modified source term into the Dirac equation yields stationary, time-independent solutions interpretable as a fermion condensate sitting just outside the horizon. If real, this would mean black holes are cloaked in a frozen fermionic halo, with implications for their thermodynamics and information content.