2008/03/06 by Thibault Damour, P. Jaranowski, Piotr Jaranowski +1 · 4 citations
Engineering · Physics and Astronomy · #Astrophysical Phenomena and Observations #Geophysics and Sensor Technology #Pulsars and Gravitational Waves Research #gr-qc
paper · pdf · doi:10.1103/physrevd.78.024009
published as Phys.Rev.D78:024009,2008 · REVTeX, 22 pages, 7 figures
arxiv created 2008/03/06 · openalex publication_date 2008/07/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the effective one body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the ``effective'' Hamiltonian and the ``real'' one; (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta; (iii) a Kerr-type effective metric (with Pad'e-resummed coefficients) which depends on the choice of some basic ``effective spin vector'' Seff, and which is deformed by comparable-mass effects; and (iv) an additional effective spin-orbit interaction term involving another spin vector \mathbit\ensuremathσ. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter \stackrel^aLSO\ensuremath≡cJLSO/(G(HLSO/c2)2). We find that the inclusion of NLO spin-orbit terms has a significant ``moderating'' effect on the dynamical characteristics of the circular orbits for large and parallel spins.