Dynamical invariants for general relativistic two-body systems at the third post-Newtonian approximation

Abstract

We extract all the invariants (i.e. all the functions which do not depend on the choice of phase-space coordinates) of the dynamics of two point-masses, at the third post-Newtonian (3PN) approximation of general relativity. We start by showing how a contact transformation can be used to reduce the 3PN higher-order Hamiltonian derived by Jaranowski and Schäfer to an ordinary Hamiltonian. The dynamical invariants for general orbits (considered in the center-of-mass frame) are then extracted by computing the radial action variable $\oint p_{r}dr$ as a function of energy and angular momentum. The important case of circular orbits is given special consideration. We discuss in detail the plausible ranges of values of the two quantities $\oms$, $\omk$ which parametrize the existence of ambiguities in the regularization of some of the divergent integrals making up the Hamiltonian. The physical applications of the invariant functions derived here (e.g. to the determination of the location of the last stable circular orbit) are left to subsequent work.

REVTeX, 21 pages, submitted to Phys. Rev. D

References in corpus (1)

• Poincaré invariance in the ADM Hamiltonian approach to the general relativistic two-body problem

Cited by in corpus (125)

• Transition from inspiral to plunge in binary black hole coalescences
• Coalescence of Two Spinning Black Holes: An Effective One-Body Approach
• Binary neutron-star mergers: a review of Einstein's richest laboratory
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• On the determination of the last stable orbit for circular general relativistic binaries at the third post-Newtonian approximation
• Black Hole Binary Dynamics from the Double Copy and Effective Theory
• A template bank for gravitational waveforms from coalescing binary black holes: non-spinning binaries
• Calibration of Moving Puncture Simulations
• Dimensional regularization of the gravitational interaction of point masses
• A Comparison of search templates for gravitational waves from binary inspiral
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Effective One Body description of tidal effects in inspiralling compact binaries
• Transition from inspiral to plunge in precessing binaries of spinning black holes
• Detecting gravitational waves from precessing binaries of spinning compact objects: Adiabatic limit
• Strong-field Gravity Tests with the Double Pulsar
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• From Boundary Data to Bound States
• Dimensional regularization of the third post-Newtonian dynamics of point particles in harmonic coordinates
• Spinning Black Hole Binary Dynamics, Scattering Amplitudes and Effective Field Theory
• Third post-Newtonian accurate generalized quasi-Keplerian parametrization for compact binaries in eccentric orbits
• Third post-Newtonian dynamics of compact binaries: Noetherian conserved quantities and equivalence between the harmonic-coordinate and ADM-Hamiltonian formalisms
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Fourth post-Newtonian effective one-body dynamics
• Phasing of gravitational waves from inspiralling eccentric binaries
• From Boundary Data to Bound States II: Scattering Angle to Dynamical Invariants (with Twist)
• Effective action approach to higher-order relativistic tidal interactions in binary systems and their effective one body description
• Detection template families for gravitational waves from the final stages of binary--black-hole inspirals: Nonspinning case
• Gravitational field and equations of motion of spinning compact binaries to 2.5 post-Newtonian order
• Equivalence between the ADM-Hamiltonian and the harmonic-coordinates approaches to the third post-Newtonian dynamics of compact binaries
• Periastron Advance in Black-Hole Binaries
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• High-accuracy numerical simulation of black-hole binaries: Computation of the gravitational-wave energy flux and comparisons with post-Newtonian approximants
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Anatomy of the binary black hole recoil: A multipolar analysis
• Frequency-domain P-approximant filters for time-truncated inspiral gravitational wave signals from compact binaries
• Gravitational radiation reaction along general orbits in the effective one-body formalism
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Tidal Effects in the Post-Minkowskian Expansion
• Classical Gravitational Scattering at $\mathcal{O}(G^3)$ from Feynman Diagrams
• Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction
• Phasing of gravitational waves from inspiralling eccentric binaries at the third-and-a-half post-Newtonian order
• Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• A physical template family for gravitational waves from precessing binaries of spinning compact objects: Application to single-spin binaries
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Dimensional regularization of local singularities in the 4th post-Newtonian two-point-mass Hamiltonian
• Circular orbits of corotating binary black holes: comparison between analytical and numerical results
• The binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM-formalism
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Energy versus Angular Momentum in Black Hole Binaries
• Quasiequilibrium sequences of synchronized and irrotational binary neutron stars in general relativity. III. Identical and different mass stars with gamma=2
• The 2PM Hamiltonian for binary Kerr to quartic in spin
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• Gravitational self-torque and spin precession in compact binaries
• Gravitational waves from black hole binary inspiral and merger: The span of third post-Newtonian effective-one-body templates
• Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit coupling
• A comparison of search templates for gravitational waves from binary inspiral - 3.5PN update
• Towards the 4th post-Newtonian Hamiltonian for two-point-mass systems
• Second post-Newtonian gravitational wave polarizations for compact binaries in elliptical orbits
• Measuring Neutron Star Radii with Gravitational Wave Detectors
• Measuring orbital eccentricity and periastron advance in quasi-circular black hole simulations
• A quasi-physical family of gravity-wave templates for precessing binaries of spinning compact objects: Application to double-spin precessing binaries
• Next-to-next-to-leading order post-Newtonian linear-in-spin binary Hamiltonians
• Mining the Geodesic Equation for Scattering Data
• First Law of Mechanics for Compact Binaries on Eccentric Orbits
• Periastron advance in spinning black hole binaries: comparing effective-one-body and Numerical Relativity
• Periastron Advance in Spinning Black Hole Binaries: Gravitational Self-Force from Numerical Relativity
• Analytic solutions of the geodesic equation in axially symmetric space-times
• First Law of Mechanics for Black Hole Binaries with Spins
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• Accuracy of gravitational waveform models for observing neutron-star--black-hole binaries in Advanced LIGO
• Symplectic Integration of Post-Newtonian Equations of Motion with Spin
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Gravitational Faraday effect from on-shell amplitudes
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Third post-Newtonian effective-one-body Hamiltonian in scalar-tensor and Einstein-scalar-Gauss-Bonnet gravity
• Circumbinary Disk Accretion into Spinning Black Hole Binaries
• The deterministic nature of conservative post-Newtonian accurate dynamics of compact binaries with leading order spin-orbit interaction
• Experimental mathematics meets gravitational self-force
• The General Relativistic Two Body Problem and the Effective One Body Formalism
• General-relativistic treatment of tidal $g$-mode resonances in coalescing binaries of neutron stars. I. Theoretical framework and crust breaking
• Bethe-Salpeter equation for classical gravitational bound states
• Second post-Newtonian Lagrangian dynamics of spinning compact binaries
• Numerical computation of the EOB potential q using self-force results
• Boundary to bound dictionary for generic Kerr orbits
• Last orbits of binary strange quark stars
• Numerical black hole initial data with low eccentricity based on post-Newtonian orbital parameters
• Binary black hole spacetimes with a helical Killing vector
• Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs
• Gauss collocation methods for efficient structure preserving integration of post-Newtonian equations of motion
• Stability and chaos of hierarchical three black hole configurations
• Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order
• General-relativistic rotation laws in rotating fluid bodies
• Effective one body Hamiltonian in scalar-tensor gravity at third post-Newtonian order
• Stringent Pulsar Timing Bounds on Light Scalar Couplings to Matter
• A skeleton approximate solution of the Einstein field equations for multiple black-hole systems
• A novel energy-conserving scheme for eight-dimensional systems
• Analytic treatment of complete geodesics in a static cylindrically symmetric conformal spacetime
• Scattering Amplitudes and N-Body Post-Minkowskian Hamiltonians in General Relativity and Beyond
• Multi-scale Constraints on Scalar-Field couplings to Matter: The Geodetic and Frame-Dragging Effects
• $f$-mode Imprints in Gravitational Waves from Coalescing Binaries involving Aligned Spinning Neutron Stars
• New class of post-Newtonian approximants to the waveform templates of inspiralling compact binaries: Test-mass in the Schwarzschild spacetime
• The final phase of inspiral of neutron stars: realistic equations of state
• Energy-conserving integrator for conservative Hamiltonian systems with ten-dimensional phase space
• Effective one-body approach to the relativistic two-body problem
• Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order
• Dirac brackets for classical radiative observables
• Measuring eccentricity in binary black-hole initial data
• Observables of a test-mass along an inclined orbit in a post-Newtonian approximated Kerr spacetime to leading-order-quadratic-in-spin
• Testing the Boundary-to-Bound Correspondence with Numerical Relativity
• A New Template Family For The Detection Of Gravitational Waves From Comparable Mass Black Hole Binaries
• Exploring the Use of Numerical Relativity Waveforms in Burst Analysis of Precessing Black Hole Mergers
• The general relativistic two body problem
• An Effective Field Theory for Binary Cosmic Strings
• Invariant-based inverse engineering for fast and robust load transport in a double pendulum bridge crane
• Complete adiabatic waveform templates for a test-mass in the Schwarzschild spacetime: VIRGO and Advanced LIGO studies
• The Eikonal Approximation and the Gravitational Dynamics of Binary Systems
• Extended mass and spheroidal deformation effects on epicyclic frequencies and periapsis shift in quasi-circular orbits
• Invariant-based inverse engineering for balanced displacement of a cart-pole system
• Unexpected Symmetries of Kerr Black Hole Scattering
• Hamiltonian normal forms for the post-Newtonian binary problem