On the perturbations of a non-rotating star excited by a massive source. I. The matching conditions at the surface of the star

Tools Share Abstract In this paper we discuss the matching conditions to be imposed at the surface of a non-rotating star, when it is perturbed by a massive source, m0 ≪ 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.