ON CRITICAL-BEHAVIOR IN GRAVITATIONAL COLLAPSE

We give an approach to studying the critical behaviour that has been o bserved in numerical studies of gravitational collapse. These studies suggest, among other things, that black holes initially form with infi nitesimal mass. We show generally how a black-hole mass formula can be extracted from a transcendental equation. Using our approach, we give an explicit one-parameter set of spherical metrics that are asymptoti cally flat, and describe the collapse of a priori unspecified but phys ical matter fields. The black-hole mass formula obtained from this met ric exhibits a mass gap-that is, at the onset of black-hole formation, the mass is finite and non-zero.