IMPOSITION OF CAUCHY DATA TO THE TEUKOLSKY EQUATION - I - THE NONROTATING CASE - ART. NO. 024015

Gravitational perturbations about a Kerr black hole in the Newman-Penr ose formalism are concisely described by the Teukolsky equation. New n umerical methods for studying the evolution of such perturbations requ ire not only the construction of appropriate initial data to describe the collision of two orbiting black holes, but also to know how such n ew data must be imposed into the Teukolsky equation, In this paper we show how Cauchy data can be incorporated explicitly into the Teukolsky equation for nonrotating black holes. The Teukolsky function Psi and its first time derivative partial derivative(t)Psi can be written in t erms of only the three-geometry and the extrinsic curvature in a gauge -invariant way. Taking a Laplace transform of the Teukolsky equation i ncorporates initial data as a source term. We show that for astrophysi cal data the straightforward Green function method leads to divergent integrals that can be regularized like for the case of a source genera ted by a particle coming from infinity. [S0556-2821(98)07614-0].