The imposition of Cauchy data to the Teukolsky equation III: The rotating case

Details The imposition of Cauchy data to the Teukolsky equation III: The rotating case The imposition of Cauchy data to the Teukolsky equation III: The rotating case

1998-03-16

arxiv.org/abs/gr-qc/9803058v1

Phys.Rev.D58:084019,1998; Erratum-ibid.D62:069901,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

5 pages, REVTEX, no figures

Scientific paper

10.1103/PhysRevD.58.084019 10.11

We solve the problem of expressing the Weyl scalars $\psi $ that describe gravitational perturbations of a Kerr black hole in terms of Cauchy data. To do so we use geometrical identities (like the Gauss-Codazzi relations) as well as Einstein equations. We are able to explicitly express $\psi $ and $\partial _t\psi $ as functions only of the extrinsic curvature and the three-metric (and geometrical objects built out of it) of a generic spacelike slice of the spacetime. These results provide the link between initial data and $\psi $ to be evolved by the Teukolsky equation, and can be used to compute the gravitational radiation generated by two orbiting black holes in the close limit approximation. They can also be used to extract waveforms from spacetimes completely generated by numerical methods.

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