Critical Behavior in Vacuum Gravitational Collapse in 4 + 1 Dimensions

摘要

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.