NEWMAN-PENROSE CONSTANTS AND THE TAILS OF SELF-GRAVITATING WAVES

We study the properties of the decay of a self-gravitating radiation f ield by analyzing the relation between behavior in the weak field regi me, test field behavior in a Schwarzschild background, and strong fiel d behavior. Our model consists of a spherically symmetric scalar field incident on a reflecting barrier, which allows all these regimes to b e treated on a common nonsingular manifold. Our primary conclusion, in the curved space case, is that there are two distinct types of late d ecay determined by whether or not the Newman-Penrose constant for the scalar field vanishes. For the nonvanishing case, the radiation tail d ecays as 1/t, with respect to Bondi time, but there are also ln t/t2 c orrections, as well as the exponentially decaying contributions associ ated with quasinormal modes.