  We construct composite CFT operators from a large number of fermionic primary
fields corresponding to states that are holographically dual to a zero
temperature Fermi gas in AdS space. We identify a large N regime in which the
fermions behave as free particles. In the hydrodynamic limit the Fermi gas
forms a degenerate star with a radius determined by the Fermi level, and a mass
and angular momentum that exactly matches the boundary calculations. Next we
consider an interacting regime, and calculate the effect of the gravitational
back-reaction on the radius and the mass of the star using the
Tolman-Oppenheimer-Volkoff equations. Ignoring other interactions, we determine
the "Chandrasekhar limit" beyond which the degenerate star (presumably)
undergoes gravitational collapse towards a black hole. This is interpreted on
the boundary as a high density phase transition from a cold baryonic phase to a
hot deconfined phase.
