Next-to-next-to-leading order gravitational spin-orbit coupling via the effective field theory for spinning objects in the post-Newtonian scheme
- Université Pierre et Marie Curie, CNRS-UMR 7095, Institut d'Astrophysique de Paris, 98 bis Boulevard Arago, 75014 Paris (France)
- Max-Planck-Institute for Gravitational Physics (Albert-Einstein-Institute), Am Mühlenberg 1, 14476 Potsdam-Golm (Germany)
We implement the effective field theory for gravitating spinning objects in the post-Newtonian scheme at the next-to-next-to-leading order level to derive the gravitational spin-orbit interaction potential at the third and a half post-Newtonian order for rapidly rotating compact objects. From the next-to-next-to-leading order interaction potential, which we obtain here in a Lagrangian form for the first time, we derive straightforwardly the corresponding Hamiltonian. The spin-orbit sector constitutes the most elaborate spin dependent sector at each order, and accordingly we encounter a proliferation of the relevant Feynman diagrams, and a significant increase of the computational complexity. We present in detail the evaluation of the interaction potential, going over all contributing Feynman diagrams. The computation is carried out in terms of the ''nonrelativistic gravitational'' fields, which are advantageous also in spin dependent sectors, together with the various gauge choices included in the effective field theory for gravitating spinning objects, which also optimize the calculation. In addition, we automatize the effective field theory computations, and carry out the automated computations in parallel. Such automated effective field theory computations would be most useful to obtain higher order post-Newtonian corrections. We compare our Hamiltonian to the ADM Hamiltonian, and arrive at a complete agreement between the ADM and effective field theory results. Finally, we provide Hamiltonians in the center of mass frame, and complete gauge invariant relations among the binding energy, angular momentum, and orbital frequency of an inspiralling binary with generic compact spinning components to third and a half post-Newtonian order. The derivation presented here is essential to obtain further higher order post-Newtonian corrections, and to reach the accuracy level required for the successful detection of gravitational radiation.
- OSTI ID:
- 22525084
- Journal Information:
- Journal of Cosmology and Astroparticle Physics, Vol. 2016, Issue 01; Other Information: Country of input: International Atomic Energy Agency (IAEA); ISSN 1475-7516
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
BINDING ENERGY
CALCULATION METHODS
COMPARATIVE EVALUATIONS
CORRECTIONS
FEYNMAN DIAGRAM
FIELD THEORIES
GAUGE INVARIANCE
GRAVITATIONAL FIELDS
GRAVITATIONAL RADIATION
HAMILTONIANS
LAGRANGIAN FUNCTION
L-S COUPLING
POTENTIALS
SPIN