Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
- 28 March 2008
- journal article
- Published by American Physical Society (APS) in Physical Review D
- Vol. 77 (6)
- https://doi.org/10.1103/physrevd.77.064032
Abstract
A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order ($G/c^4$ and $G^2/c^4$) in the spin-orbit interaction. We use a novel approach (valid to linear order in the spins), which starts from the second-post-Newtonian metric (in ADM coordinates) generated by two spinless bodies, and computes the next-to-leading order precession, in this metric, of suitably redefined ``constant-magnitude'' 3-dimensional spin vectors ${\bf S}_1$, ${\bf S}_2$. We prove the Poincar\'e invariance of our Hamiltonian by explicitly constructing ten phase-space generators realizing the Poincar\'e algebra. A remarkable feature of our approach is that it allows one to derive the {\it orbital} equations of motion of spinning binaries to next-to-leading order in spin-orbit coupling without having to solve Einstein's field equations with a spin-dependent stress tensor. We show that our Hamiltonian (orbital and spin) dynamics is equivalent to the dynamics recently obtained by Faye, Blanchet, and Buonanno, by solving Einstein's equations in harmonic coordinates.Comment: Few minor corrections made, 2 references added, some misprints remove
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This publication has 23 references indexed in Scilit:
- Erratum: Higher-order spin effects in the dynamics of compact binaries. II. Radiation field [Phys. Rev. D74, 104034 (2006)]Physical Review D, 2007
- Higher-order spin effects in the dynamics of compact binaries. I. Equations of motionPhysical Review D, 2006
- Higher-order spin effects in the dynamics of compact binaries. II. Radiation fieldPhysical Review D, 2006
- Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian orderPhysical Review D, 2001
- Coalescing binary systems of compact objects to (post-Newtonian order. V. Spin effectsPhysical Review D, 1995
- Spin effects in the inspiral of coalescing compact binariesPhysical Review D, 1993
- The gravitational interaction: Spin, rotation, and quantum effects-a reviewGeneral Relativity and Gravitation, 1979
- Interaction of two black holes in the slow-motion limitPhysical Review D, 1975
- Gravitational two-body problem with arbitrary masses, spins, and quadrupole momentsPhysical Review D, 1975
- Spinning test-particles in general relativity. IProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1951