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 sourc e, m(0) << M, either orbiting around the star or scattered by it. We s hall determine the relations existing among the Regge-Wheeler and the Zerilli functions, which can be constructed by integrating the equatio ns in the interior of the star, and the Bardeen-Press-Teukolsy and the Nakamura-Sasaki functions. which describe the perturbation outside th e star, in the framework of the Newman-Penrose formalism. We shall als o find the general form of the solution of the Nakamura-Sasaki equatio n appropriate to describe the problem on hand, by the Green's function method.