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We apply a new analytic scheme, developed in a preceding paper, in order tocalculate the late time behavior of scalar test fields evolving outside aSchwarzschild black hole. The pattern of the late time decay at future nullinfinity is found to be the same as in the shell toy-model studied in thepreceding 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 thelate time wave behavior anywhere outside the black hole. This reproduces thewell 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 itsapplicability to rotating black holes, as shall be discussed in a forthcomingpaper.Comment: 17 pages, 14 figures. Accepted for publication in Physical Review

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