  We present a new analytic approach for the study of late time evolution of
linear test-fields, propagating on the exterior of black holes. This method
provides a calculation scheme applicable to Kerr black holes (for which case no
analytic calculation of the late time tails has been presented so far). In this
paper we develop the new technique and apply it to the case of massless scalar
waves evolving on the background geometry of a static spherically-symmetric
thin shell with a Schwarzschild exterior. The late time behavior of the scalar
field at null infinity is calculated, and is explicitly related to the form of
(quite arbitrary) initial data. This reproduces the well-known late time
power-law decaying tails. In an accompanying paper we apply our approach to the
complete Schwarzschild black hole geometry, where we obtain the familiar
inverse-power late time tails at null infinity, as well as at time-like
infinity and along the event horizon. A calculation of the late time power-law
tails in the Kerr geometry, based on the same approach, will be presented in a
forthcoming paper.
