Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling

By T. Damour, P. Jaranowski, G. Schāfer. 2007

145 citations recorded by the source corpus.

A Hamiltonian formulation is given for the gravitational dynamics of two spinning compact bodies to next-to-leading order (G/c{sup 4} and G{sup 2}/c{sup 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 Arnowitt-Deser-Misner 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 S{sub 1}, S{sub 2}. We prove the Poincare invariance of our Hamiltonian by explicitly constructing 10 phase-space generators realizing the Poincare algebra. A remarkable feature of our approach is that it allows one to derive the 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.

Subfields: Astronomy and Astrophysics, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/6e9532350a7edd88d277fa375bde2abafbcdc56e

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In Astronomy and Astrophysics

1. T. Damour
2. J. Steinhoff
3. G. Schāfer
4. P. Jaranowski
5. M. Levi
6. Rafael A. Porto
7. L. Blanchet
8. J. Vines

In Atomic and Molecular Physics, and Optics

1. T. Damour
2. J. Steinhoff
3. M. Levi
4. G. Schāfer
5. P. Jaranowski
6. Rafael A. Porto
7. C. Will
8. L. Blanchet

Citations in the corpus

• Spinning gravitating objects in the effective field theory in the post-Newtonian scheme (2015, methodology): “To verify equivalence with the ADM Hamiltonian result, which was first obtained in [59], after the corresponding EOM were obtained in [56, 68], we resolve the difference between the result in [59], and the result here, using canonical transformations, see e.”
• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling (2008, methodology): “In the present paper, we extend and refine the EOB description of spinning binaries by using a recently derived [13] Hamiltonian description of the spin-orbit interaction valid at the next to leading order (NLO) in the PN expansion.”