Abstract
We reexamine the question of the imposition of initial data representing 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 express the Teukolsky function explicitly in terms of hypersurface quantities, we relate it to the Moncrief waveform through a Chandrasekhar transformation in the case of a nonrotating black hole. This relation between and holds for any constant time hypersurface and allows us to compare the computation of the evolution of Schwarzschild perturbations by the Teukolsky and by the Zerilli and Regge-Wheeler equations. We explicitly perform this comparison for the Misner initial data in the close limit approach. We evolve numerically both the Teukolsky (with the recent code of Krivan et al.) and the Zerilli equations, finding complete agreement in resulting waveforms within numerical error. The consistency of these results further supports the correctness of the numerical code for evolving the Teukolsky equation as well as the analytic expressions for in terms only of the three-metric and the extrinsic curvature.
- Received 20 January 1998
DOI:https://doi.org/10.1103/PhysRevD.58.024016
©1998 American Physical Society