# The Kerr-Fermi Sea

## TL;DR

This paper demonstrates that massive fermions around a Kerr black hole form a Fermi sea instead of causing instability, with properties analytically derived using semiclassical methods.

## Contribution

It introduces the concept of a Fermi sea formed by fermions near a Kerr black hole, contrasting with scalar fields that induce instabilities, and provides analytical descriptions of its properties.

## Key findings

- Fermi sea extends outside the ergosphere.
- Analytical shape and properties of the Fermi sea are derived.
- Effective theory describes ripples in the Fermi surface.

## Abstract

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.