The Carter constant for inclined orbits about a massive Kerr black hole: near-circular, near-polar orbits

Open Physics - 2012
P.G. Komorowski1, S. R. Valluri2, Martin Houde1
1Department of Physics and Astronomy, University of Western Ontario, 1151 Richmond Street, London, Ontario, N6A 3K7, Canada
2Department of Physics and Astronomy, Department of Applied Mathematics, University of Western Ontario, 1151 Richmond Street, London, Ontario, N6A 3K7, Canada

Tóm tắt

AbstractIn an extreme mass-ratio binary black hole system, a non-equatorial orbit will list (i.e. increase its angle of inclination, i) as it evolves in Kerr spacetime. The abutment, a set of evolving, near-polar, retrograde orbits, for which the instantaneous Carter constant (Q) is at its maximum value (Q X) for given values of latus rectum (l̃) and eccentricity (e), has been introduced as a laboratory in which the consistency of dQ/dt with corresponding evolution equations for d l̃/dt and de/dt might be tested independently of a specific radiation back-reaction model. To demonstrate the use of the abutment as such a laboratory, a derivation of dQ/dt, based only on published formulae for d l̃/dt and de/dt, was performed for elliptical orbits on the abutment. The resulting expression for dQ/dt matched the published result to the second order in e. We believe the abutment is a potentially useful tool for improving the accuracy of evolution equations to higher orders of e and l̃−.

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