General Relativistic Dynamics of Compact Binary Systems

Abstract

The equations of motion of compact binary systems have been derived in the post-Newtonian (PN) approximation of general relativity. The current level of accuracy is 3.5PN order. The conservative part of the equations of motion (neglecting the radiation reaction damping terms) is deducible from a generalized Lagrangian in harmonic coordinates, or equivalently from an ordinary Hamiltonian in ADM coordinates. As an application we investigate the problem of the dynamical stability of circular binary orbits against gravitational perturbations up to the 3PN order. We find that there is no innermost stable circular orbit or ISCO at the 3PN order for equal masses.

13 pages, to appear in the special issue of the Comptes rendus de l'Academie des Sciences de Paris on "Observations of black holes and extreme gravitational events", edited by Daniel Rouan

References in corpus (24)

• Effective one-body approach to general relativistic two-body dynamics
• Spin effects in the inspiral of coalescing compact binaries
• Improved filters for gravitational waves from inspiralling compact binaries
• Dimensional regularization of the gravitational interaction of point masses
• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• General relativistic dynamics of compact binaries at the third post-Newtonian order
• Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. II. Two-body equations of motion to second post-Newtonian order, and radiation-reaction to 3.5 post-Newtonian order
• Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order
• A Post-Newtonian diagnostic of quasi-equilibrium binary configurations of compact objects
• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem
• Third post-Newtonian dynamics of compact binaries: Equations of motion in the center-of-mass frame
• Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries
• Hadamard Regularization
• New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
• The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part
• On the equations of motion of point-particle binaries at the third post-Newtonian order
• Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
• Innermost circular orbit of binary black holes at the third post-Newtonian approximation
• Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
• The binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM-formalism
• Equation of motion for relativistic compact binaries with the strong field point particle limit : the second and half post-Newtonian order
• Lorentzian regularization and the problem of point-like particles in general relativity

Cited by in corpus (3)

• Hierarchical data-driven approach to fitting numerical relativity data for nonprecessing binary black holes with an application to final spin and radiated energy
• Conservative self-force correction to the innermost stable circular orbit: comparison with multiple post-Newtonian-based methods
• On the role of magnetic fields into the dynamics and gravitational wave emission of binary neutron stars