The Kerr-Fermi Sea

The presence of a massive scalar field near a Kerr black hole is known to produce instabilities associated with bound superradiant modes. In this paper we show that for massive fermions, rather than inducing an instability, the bound superradiant modes condense and form a Fermi sea which extends well outside the ergosphere. The shape of this Fermi sea in phase space and various other properties are analytically computed in the semiclassical WKB approximation. The low energy effective theory near the black hole is described by ripples in the Fermi surface. Expressions are derived for their dispersion relation and the effective force on particles which venture into the sea.