The imposition of Cauchy data to the Teukolsky equation II: Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations

Abstract

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.

14 pages, 7 Postscript figures, to appear in Phys. Rev. D

References in corpus (4)

• Evolving the Bowen-York initial data for spinning black holes
• Black Hole Data via a Kerr-Schild Approach
• Improved initial data for black hole collisions
• The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case

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• Retarded radiation from colliding black holes in the close limit
• Persistent junk solutions in time-domain modeling of extreme mass ratio binaries
• The imposition of Cauchy data to the Teukolsky equation III: The rotating case
• The close limit from a null point of view: the advanced solution
• The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case
• Perturbative evolution of nonlinear initial data for binary black holes: Zerilli vs. Teukolsky