Celestial mechanics in Kerr spacetime

By W. Schmidt. 2002

195 citations recorded by the source corpus.

The dynamical parameters conventionally used to specify the orbit of a test particle in Kerr spacetime are the energy E, the axial component of the angular momentum, Lz, and Carter's constant Q. These parameters are obtained by solving the Hamilton?Jacobi equation for the dynamical problem of geodesic motion. Employing the action-angle variable formalism, on the other hand, yields a different set of constants of motion, namely, the fundamental frequencies ?r, ?? and ? associated with the radial, polar and azimuthal components of orbital motion, respectively. These frequencies, naturally, determine the time scales of orbital motion and, furthermore, the instantaneous gravitational wave spectrum in the adiabatic approximation. In this paper, it is shown that the fundamental frequencies are geometric invariants and explicit formulae in terms of quadratures are derived. The numerical evaluation of these formulae in the case of a rapidly rotating black hole illustrates the behaviour of the fundamental frequencies as orbital parameters, such as the semi-latus rectum p, the eccentricity e or the inclination parameter ?? are varied. The limiting cases of circular, equatorial and Keplerian motion are investigated as well and it is shown that known results are recovered from the general formulae.

Subfields: Astronomy and Astrophysics, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/2f7287e2b1f523c27831936bbe01abceac6a520b

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In Astronomy and Astrophysics

1. A. Pound
2. B. Wardell
3. T. Hinderer
4. E. Flanagan
5. S. Drasco
6. S. Hughes
7. E. Poisson
8. Kent Yagi

In Ocean Engineering

1. T. Hinderer
2. S. Drasco
3. E. Flanagan
4. B. Wardell
5. A. Pound
6. S. Hughes
7. Rafael A. Porto
8. Luca Baiotti

Citations in the corpus

• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion (2008, methodology): “Following Schmidt [93], we can obtain an invertible transformation from the Boyer-Lindquist phase space coordinates (x , pν) to the generalized action angle variables (qα, Jα) as follows.”
• Black hole perturbation theory and gravitational self-force (2021, methodology): “[178, 128, 57, 58, 65, 203, 182] for additional details about geodesic orbits in Kerr.”
• Gravitational wave snapshots of generic extreme mass ratio inspirals (2005, methodology): “[45] W. Schmidt, Celestial mechanics in Kerr spacetime, Class.”