LATE-TIME BEHAVIOR OF STELLAR COLLAPSE AND EXPLOSIONS .1. LINEARIZED PERTURBATIONS

We study the power-law tails in the evolution of massless fields aroun d a fixed background geometry corresponding to a black hole: We give a nalytical arguments for their existence at scri(+), at the future hori zon, and at future timelike infinity. We confirm their existence with numerical integrations of the curved spacetime wave equation on the ba ckground of a Schwarzschild and a Reissner-Nordstrom black hole. These results are relevant to studies of mass inflation and the instability of Cauchy horizons. The analytic arguments also suggest the behavior of the full nonlinear dynamics, which we study numerically in a compan ion paper.