Critical behavior in vacuum gravitational collapse in 4+1 dimensions
  We show that the 4+1 dimensional vacuum Einstein equations admit gravitational waves with radial symmetry. The dynamical degrees of freedom correspond to deformations of the three-sphere orthogonal to the $(t,r)$ plane. Gravitational collapse of such waves is studied numerically and shown to exhibit discretely self-similar Type II critical behavior at the threshold of black hole formation. 
Piotr Bizo\'n, Tadeusz Chmaj, Bernd G. Schmidt