  We revisit 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 Psi explicitly in terms of hypersurface quantities, we relate it to
the Moncrief waveform phi_M through a Chandrasekhar transformation in the case
of a nonrotating black hole. This relation between Psi and phi_M 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 Ref. [1]) 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 Psi in terms only of the three-metric and the extrinsic curvature.
