IMPOSITION OF CAUCHY DATA TO THE TEUKOLSKY EQUATION - II - NUMERICAL COMPARISON WITH THE ZERILLI-MONCRIEF APPROACH TO BLACK-HOLE PERTURBATIONS - ART. NO. 024016

We reexamine the question of the imposition of initial data representi ng astrophysical gravitational perturbations of black holes. We study their dynamics for the case of nonrotating black holes by numerically evolving the Teukolsky equation in the time domain. In order to expres s the Teukolsky function Psi explicitly in terms of hypersurface quant ities, we relate it to the Moncrief waveform phi(M) through a Chandras ekhar transformation in the case of a nonrotating black hole. This rel ation between Psi and phi(M) holds for any constant time hypersurface and allows us to compare the computation of the evolution of Schwarzsc hild perturbations by the Teukolsky and by the Zerilli and Regge-Wheel er equations. We explicitly perform this comparison for the Misner ini tial data in the close limit approach. We evolve numerically both the Teukolsky (with the recent code of Krivan et al.) and the Zerilli equa tions, finding complete agreement in resulting waveforms within numeri cal error. The consistency of these results further supports the corre ctness of the numerical code for evolving the Teukolsky equation as we ll as the analytic expressions for Psi in terms only of the three-metr ic and the extrinsic curvature. [S0556-2821(98)07314-7].