Late time dynamics of scalar perturbations outside black holes: II.   Schwarzschild geometry
  We apply a new analytic scheme, developed in a preceding 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 preceding 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 time-like 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. 
Leor Barack