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Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling


Balmelli, Simone; Jetzer, Philippe (2015). Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling. Physical Review D (Particles, Fields, Gravitation and Cosmology), 91:064011.

Abstract

We propose a way of including the next-to-leading (NLO) order spin-spin coupling in an effective-one-body (EOB) Hamiltonian. This work extends by S. Balmelli and P. Jetzer, [Phys. Rev. D 87, 124036 (2013)], which is restricted to the case of equatorial orbits and aligned spins, to general orbits with arbitrary spin orientations. This is done by applying appropriate canonical phase-space transformations to the NLO spin-spin Hamiltonian in Arnowitt-Deser-Misner (ADM) coordinates, and systematically adding effective quantities at NLO to all spin-squared terms appearing in the EOB Hamiltonian. As required by consistency, the introduced quantities reduce to zero in the test-mass limit. We expose the result both in a general gauge and in a gauge-fixed form. The last is chosen such as to minimize the number of new coefficients that have to be inserted into the effective spin squared. As a result, the 25 parameters that describe the ADM NLO spin-spin dynamics get condensed into only 12 EOB terms.

Abstract

We propose a way of including the next-to-leading (NLO) order spin-spin coupling in an effective-one-body (EOB) Hamiltonian. This work extends by S. Balmelli and P. Jetzer, [Phys. Rev. D 87, 124036 (2013)], which is restricted to the case of equatorial orbits and aligned spins, to general orbits with arbitrary spin orientations. This is done by applying appropriate canonical phase-space transformations to the NLO spin-spin Hamiltonian in Arnowitt-Deser-Misner (ADM) coordinates, and systematically adding effective quantities at NLO to all spin-squared terms appearing in the EOB Hamiltonian. As required by consistency, the introduced quantities reduce to zero in the test-mass limit. We expose the result both in a general gauge and in a gauge-fixed form. The last is chosen such as to minimize the number of new coefficients that have to be inserted into the effective spin squared. As a result, the 25 parameters that describe the ADM NLO spin-spin dynamics get condensed into only 12 EOB terms.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Language:English
Date:4 February 2015
Deposited On:12 Feb 2016 15:21
Last Modified:05 Apr 2016 20:03
Publisher:American Physical Society
ISSN:1550-2368
Publisher DOI:https://doi.org/10.1103/PhysRevD.91.064011
Other Identification Number:arXiv:1502.01343v1

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