The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case

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 non-rotating black holes. The Teukolsky function and its first time derivative ${\partial }_t\Psi$ can be written in terms of only the 3-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.

9 pages, REVTEX. Misprints corrected in formulas (2.4)-(2.7). Final version to appear in PRD

References in corpus (7)

• Dynamics of perturbations of rotating black holes
• Understanding initial data for black hole collisions
• Black Hole Data via a Kerr-Schild Approach
• Improved initial data for black hole collisions
• The imposition of Cauchy data to the Teukolsky equation III: The rotating case
• The imposition of Cauchy data to the Teukolsky equation II: Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations
• Regularization of the Teukolsky Equation for Rotating Black Holes

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