IMPOSITION OF CAUCHY DATA TO THE TEUKOLSKY EQUATION - III - THE ROTATING CASE - ART. NO. 084019

We solve the problem of expressing the Weyl scalars psi that describe gravitational perturbations of a Ken black hole in terms of Cauchy dat a. To do so we use geometrical identities (such as the Gauss-Codazzi r elations as well as the Einstein equations. We are able to explicitly express psi and partial derivative(t)psi as functions only of the extr insic curvature and the three-metric land geometrical objects built ou t of it) of a generic spacelike slice of the spacetime. These results provide the link between initial data and psi to be evolved by the Teu kolsky equation, and can be used to compute the gravitational radiatio n generated by two orbiting black holes in the close limit approximati on. They can also be used to extract wave forms from numerically gener ated space times. [S0556-2821(98)00420-2].