Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1997-11-04
Phys.Rev. D58 (1998) 024015
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
9 pages, REVTEX. Misprints corrected in formulas (2.4)-(2.7). Final version to appear in PRD
Scientific paper
10.1103/PhysRevD.58.024015
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 $% \Psi $ 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.
Campanelli Manuela
Lousto Carlos O.
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