Late time dynamics of scalar perturbations outside black holes. II. Schwarzschild geometry

We apply a new analytic scheme, developed in a previous paper, in order to calculate the late time behavior of scalar test fields evolving outside a Schwarzschild black hole. The pattern of the late time decay at future null infinity is found to be the same as in the shell toy model studied in the previous paper. A simple late time expansion of the scalar field is then used, relying on the results at null infinity, to construct a complete picture of the late time wave behavior anywhere outside the black hole. This reproduces the well known power-law tails at timelike infinity and along the event horizon. The main motivation for the introduction of the new approach arises from its applicability to rotating black holes, as shall be discussed in a forthcoming paper.