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

Manuela Campanelli*

Carlos O. Lousto†

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

  • 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: lousto@iafe.uba.ar
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Phys. Rev. D 58, 024015 – Published 25 June, 1998

DOI: https://doi.org/10.1103/PhysRevD.58.024015

Abstract

Gravitational perturbations about a Kerr black hole in the Newman-Penrose formalism are concisely described by the Teukolsky equation. New numerical methods for studying the evolution of such perturbations require not only the construction of appropriate initial data to describe the collision of two orbiting black holes, but also to know how such new data must be imposed into the Teukolsky equation. In this paper we show how Cauchy data can be incorporated explicitly into the Teukolsky equation for nonrotating black holes. The Teukolsky function Ψ and its first time derivative ∂tΨ can be written in terms of only the three-geometry and the extrinsic curvature in a gauge-invariant way. Taking a Laplace transform of the Teukolsky equation incorporates initial data as a source term. We show that for astrophysical data the straightforward Green function method leads to divergent integrals that can be regularized like for the case of a source generated by a particle coming from infinity.

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See Also

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

Manuela Campanelli, William Krivan, and Carlos O. Lousto
Phys. Rev. D 58, 024016 (1998)

Imposition of Cauchy data to the Teukolsky equation. III. The rotating case

Manuela Campanelli, Carlos O. Lousto, John Baker, Gaurav Khanna, and Jorge Pullin
Phys. Rev. D 58, 084019 (1998)

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Phys. Rev. D 58, 024015– Published 25 June, 1998
  • Received 4 November 1997

© 1998 American Physical Society

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