New effective-one-body Hamiltonian with next-to-leading order spin-spin coupling

2015/09/27 by Simone Balmelli, Thibault Damour · 35 citations
Mathematics · Physics and Astronomy · #Angular momentum #Black Holes and Theoretical Physics #Condensed matter physics #Gauge theory #Hamiltonian (control theory) #Mathematical physics #Mathematics #Physics #Pulsars and Gravitational Waves Research #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Spin (aerodynamics) #Spins #Theoretical physics #gr-qc

paper · pdf · doi:10.1103/physrevd.92.124022

published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 92(12) (American Physical Society) · 18 pages, 6 figures. Submitted to Physical Review D

arxiv created 2015/09/27 · openalex publication_date 2015/12/11 · arxiv updated 2016/01/20 · openalex created_date 2022/05/12 · openalex updated_date 2026/08/05

Abstract

We present a new effective-one-body (EOB) Hamiltonian with next-to-leading order (NLO) spin-spin coupling for black hole binaries endowed with arbitrarily oriented spins. The Hamiltonian is based on the model for parallel spins and equatorial orbits developed in [Physical Review D 90, 044018 (2014)] but differs from it in several ways. In particular, the NLO spin-spin coupling is not incorporated by a redefinition of the centrifugal radius r_c but by separately modifying certain sectors of the Hamiltonian, which are identified according to their dependence on the momentum vector. The gauge-fixing procedure we follow allows us to reduce the 25 different terms of the NLO spin-spin Hamiltonian in Arnowitt--Deser--Misner coordinates to only nine EOB terms. This is an improvement with respect to the EOB model recently proposed in [Physical Review D 91, 064011 (2015)], where 12 EOB terms were involved. Another important advantage is the remarkably simple momentum structure of the spin-spin terms in the effective Hamiltonian, which is simply quadratic up to an overall square root. Moreover, a Damour--Jaranowski--Sch"afer-type gauge could be established, thus allowing one to concentrate, in the case of circular and equatorial orbits, the whole spin-spin interaction in a single radial potential.

Citations

• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
• Two-body gravitational spin-orbit interaction at linear order in the mass ratio
• Canonical formulation of self-gravitating spinning-object systems
• Effective one-body approach to general relativistic two-body dynamics
• Improved effective-one-body Hamiltonian for spinning black-hole binaries
• Determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation