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Imposition of Cauchy data to the Teukolsky equation. II. Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations

Manuela Campanelli*

William Krivan†

Carlos O. Lousto‡

  • Department of Physics, University of Utah, 201 JFB, Salt Lake City, Utah 84112

  • Department of Physics, University of Utah, 201 JFB, Salt Lake City, Utah 84112
  • Institut für Astronomie und Astrophysik, Universität Tübingen, D-72076 Tübingen, Germany

  • Instituto de Astronomía y Física del Espacio, Casilla de Correo 67, Sucursal 28, (1428) Buenos Aires, Argentina

  • *Electronic address: manuela@mail.physics.utah.edu
  • †Electronic address: krivan@mail.physics.utah.edu
  • ‡Electronic address: lousto@iafe.uba.ar
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Phys. Rev. D 58, 024016 – Published 25 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.024016

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 Ψ explicitly in terms of hypersurface quantities, we relate it to the Moncrief waveform φM through a Chandrasekhar transformation in the case of a nonrotating black hole. This relation between Ψ and φM 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 Ψ in terms only of the three-metric and the extrinsic curvature.

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See Also

Imposition of Cauchy data to the Teukolsky equation. I. The nonrotating case

Manuela Campanelli and Carlos O. Lousto
Phys. Rev. D 58, 024015 (1998)

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Phys. Rev. D 58, 024016– Published 25 June, 1998
  • Received 20 January 1998

© 1998 American Physical Society

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