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

Abstract

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.

5 pages, REVTEX, no figures

References in corpus (3)

• Dynamics of perturbations of rotating black holes
• The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case
• The imposition of Cauchy data to the Teukolsky equation II: Numerical comparison with the Zerilli-Moncrief approach to black hole perturbations

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• Retarded radiation from colliding black holes in the close limit
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• Perturbations of the Kerr spacetime in horizon penetrating coordinates
• The close limit from a null point of view: the advanced solution
• The imposition of Cauchy data to the Teukolsky equation I: The nonrotating case
• Perturbative evolution of nonlinear initial data for binary black holes: Zerilli vs. Teukolsky
• Collision of spinning black holes in the close limit: The parallel spin case
• Evolution of Kerr-Schild type initial data for binary black holes using the horizon penetrating Teukolsky equation