Collapse to a rotating black hole

Abstract

A slowly rotating black hole is shown to form as a result of gravitational collapse of a dust cloud. The exterior vacuum region is that of the Kerr metric with small rotation parameter at all stages of the collapse; in particular, there is no gravitational radiation. A linearized perturbation of the closed Friedmann-Robertson-Walker dust cloud provides the interior region of the spacetime and matches smoothly to the Kerr exterior. The geometry is shown to be regular on the event horizon. Dragging of inertial frames during the collapse is discussed.