Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order

Abstract

The recently constructed Hamiltonians for spinless binary black holes through third post-Newtonian order and for spinning ones through formal second post-Newtonian order, where the spins are counted of zero post-Newtonian order, are transformed into fully canonical center-of-mass and rest-frame variables. The mixture terms in the Hamiltonians between center-of-mass and rest-frame variables are in accordance with the relation between the total linear momentum and the center-of-mass velocity as demanded by global Lorentz invariance. The various generating functions for the center-of-mass and rest-frame canonical variables are explicitly given in terms of the single-particle canonical variables. The no-interaction theorem does not apply because the world-line condition of Lorentz covariant position variables is not imposed.

arXiv comment18 pages, no figures

References in corpus (14)

• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Dimensional regularization of the gravitational interaction of point masses
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• xPerm: fast index canonicalization for tensor computer algebra
• Hamiltonian of two spinning compact bodies with next-to-leading order gravitational spin-orbit coupling
• Effective one body approach to the dynamics of two spinning black holes with next-to-leading order spin-orbit coupling
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation
• Spin-squared Hamiltonian of next-to-leading order gravitational interaction
• ADM canonical formalism for gravitating spinning objects
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Higher-order-in-spin interaction Hamiltonians for binary black holes from source terms of Kerr geometry in approximate ADM coordinates
• Hamiltonian Relativistic Two-Body Problem: Center of Mass and Orbit Reconstruction
• Canonical formulation of gravitating spinning objects at 3.5 post-Newtonian order

Cited by in corpus (8)

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• Deviation of quadrupolar bodies from geodesic motion in a Kerr spacetime
• The secular evolution of discrete quasi-Keplerian systems. II. Application to a multi-mass axisymmetric disc around a supermassive black hole
• Canonical center and relative coordinates for compact binary systems through second post-Newtonian order
• Hamiltonian normal forms for the post-Newtonian binary problem