Black holes: A physical route to the Kerr metric
  As a consequence of Birkhoff's theorem, the exterior gravitational field of a spherically symmetric star or black hole is always given by the Schwarzschild metric. In contrast, the exterior gravitational field of a rotating (axisymmetric) star differs, in general, from the Kerr metric, which describes a stationary, rotating black hole.   In this paper, I discuss the possibility of a quasi-stationary transition from rotating equilibrium configurations of normal matter to rotating black holes. 
R. Meinel