On the perturbations of a nonrotating star excited by a massive source .1. The matching conditions at the surface of the star

In this paper we discuss the matching conditions to be imposed at the surface of a nonrotating star, when it is perturbed by a massive source, m(0) << M, either orbiting around the star or scattered by it. We shall determine the relations existing among the Regge-Wheeler and the Zerilli functions, which can be constructed by integrating the equations in the interior of the star, and the Bardeen-Press-Teukolsy and the Nakamura-Sasaki functions. which describe the perturbation outside the star, in the framework of the Newman-Penrose formalism. We shall also find the general form of the solution of the Nakamura-Sasaki equation appropriate to describe the problem on hand, by the Green's function method.