HIGH AMPLITUDE LIMIT OF SCALAR POWER

For spherically symmetric, massless Einstein-Klein-Gordon fields we sh ow that the scalar radiation power saturates at high amplitude at the universal value pi/32, independent of the interior structure of the fi eld. This provides a framework for understanding the energetics of sel f-gravitating effects in which our high-amplitude limits complement th e low-amplitude predictions of linearized theory. The gravitational co llapse of a high-amplitude initial state to a black hole is studied.