Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach

2010/06/30 by Michèle Levi, Michele Levi · 124 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Classical mechanics #Cosmology and Gravitation Theories #Covariant transformation #Effective field theory #Equations of motion #Formalism (music) #Gravitation #Gravitational field #Hamiltonian (control theory) #Mathematics #Parametrization (atmospheric modeling) #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Spin–orbit interaction #Theoretical physics #gr-qc #hep-th

paper · pdf · doi:10.1103/physrevd.82.104004

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 82(10) (American Physical Society) · 27 pages, revtex4-1, 4 figures; v2: minor editing made; v3: published

arxiv created 2010/11/03 · openalex publication_date 2010/11/03 · arxiv updated 2010/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We use an effective field theory (EFT) approach to calculate the next-to-leading order (NLO) gravitational spin-orbit interaction between two spinning compact objects. The NLO spin-orbit interaction provides the most computationally complex sector of the NLO spin effects, previously derived within the EFT approach. In particular, it requires the inclusion of nonstationary cubic self-gravitational interaction, as well as the implementation of a spin supplementary condition (SSC) at higher orders. The EFT calculation is carried out in terms of the nonrelativistic gravitational field parametrization, making the calculation more efficient with no need to rely on automated computations, and illustrating the coupling hierarchy of the different gravitational field components to the spin and mass sources. Finally, we show explicitly how to relate the EFT derived spin results to the canonical results obtained with the Arnowitt-Deser-Misner (ADM) Hamiltonian formalism. This is done using noncanonical transformations, required due to the implementation of covariant SSC, as well as canonical transformations at the level of the Hamiltonian, with no need to resort to the equations of motion or the Dirac brackets.

Citations

• Localized States for Elementary Systems
• The reduced Hamiltonian for next-to-leading-order spin-squared dynamics of general compact binaries
• Spinning test-particles in general relativity. I
• Canonical formulation of self-gravitating spinning-object systems
• Higher-order spin effects in the dynamics of compact binaries. I. Equations of motion
• The mass-centre in the restricted theory of relativity and its connexion with the quantum theory of elementary particles
• Les Houches Lectures on Effective Field Theories and Gravitational Radiation
• Gravitational Radiation from Post-Newtonian Sources and Inspiralling Compact Binaries

Cited by

• Next-to-next-to-leading order post-Newtonian spin-orbit Hamiltonian for self-gravitating binaries
• Influence of internal structure on the motion of test bodies in extreme mass ratio situations
• Next-to-next-to-leading order spin–orbit effects in the gravitational wave flux and orbital phasing of compact binaries
• Asymptotic dynamics on the worldline for spinning particles