Constants of motion in gravitational self-force theory

Abstract

Synergies between self-force theory and other approaches to the gravitational two-body problem have traditionally relied on calculations of gauge-invariant observables as functions of orbital frequencies. However, in self-force theory, one can also define a complete set of constants of motion: energy, azimuthal angular momentum, and radial and polar actions. Here, we outline how directly utilizing these constants allows for more straightforward comparisons and hybridizations across the parameter space, as well as more streamlined waveform generation through flux-balance laws. Restricting to the case of nonspinning binaries and first order in self-force, we compute the constants of motion and the corrections to fundamental frequencies numerically as well as analytically (to 9PN in a post-Newtonian expansion), establishing consistency with the highest-order (4PN) results available from post-Newtonian theory. We also apply the results to identify the perturbed locations of special curves in the parameter space: circular orbits and the separatrix between bound and plunging orbits.

19 pages + Appendices, 5 figures. v2: minor updates and correction of "data_separatrix$.$csv". v3: minor updates and correction of "PN_expressions.wl" (matches published version)

References in corpus (126)

• SciPy 1.0--Fundamental Algorithms for Scientific Computing in Python
• Effective one-body approach to general relativistic two-body dynamics
• Transition from inspiral to plunge in binary black hole coalescences
• Isolated and dynamical horizons and their applications
• A simple model of complete precessing black-hole-binary gravitational waveforms
• Inspiral-merger-ringdown waveforms for black-hole binaries with non-precessing spins
• Computationally efficient models for the dominant and sub-dominant harmonic modes of precessing binary black holes
• Matching post-Newtonian and numerical relativity waveforms: systematic errors and a new phenomenological model for non-precessing black hole binaries
• Self-force and radiation reaction in general relativity
• Self-force via a Green's function decomposition
• Analytic black hole perturbation approach to gravitational radiation
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• Two timescale analysis of extreme mass ratio inspirals in Kerr. I. Orbital Motion
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Surrogate model of hybridized numerical relativity binary black hole waveforms
• First higher-multipole model of gravitational waves from spinning and coalescing black-hole binaries
• Faithful Effective-One-Body waveforms of small-mass-ratio coalescing black-hole binaries
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• Celestial mechanics in Kerr spacetime
• FastEMRIWaveforms: New tools for millihertz gravitational-wave data analysis
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• A Periodic Table for Black Hole Orbits
• Analytical solutions of bound timelike geodesic orbits in Kerr spacetime
• Gravitational self-force on a particle in eccentric orbit around a Schwarzschild black hole
• Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
• SEOBNRv5PHM: Next generation of accurate and efficient multipolar precessing-spin effective-one-body waveforms for binary black holes
• Laying the foundation of the effective-one-body waveform models SEOBNRv5: improved accuracy and efficiency for spinning non-precessing binary black holes
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Eccentric, nonspinning, inspiral, Gaussian-process merger approximant for the detection and characterization of eccentric binary black hole mergers
• Novel approach to binary dynamics: application to the fifth post-Newtonian level
• Gravitational waveforms for compact binaries from second-order self-force theory
• Rapid generation of fully relativistic extreme-mass-ratio-inspiral waveform templates for LISA data analysis
• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Second-order gravitational self-force
• The complete non-spinning effective-one-body metric at linear order in the mass ratio
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Gravitational radiation reaction and inspiral waveforms in the adiabatic limit
• Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits
• Adiabatic waveforms for extreme mass-ratio inspirals via multivoice decomposition in time and frequency
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux
• Precession effect of the gravitational self-force in a Schwarzschild spacetime and the effective one-body formalism
• Symmetries and charges of general relativity at null boundaries
• Beyond the geodesic approximation: conservative effects of the gravitational self-force in eccentric orbits around a Schwarzschild black hole
• Gravitational-wave energy flux for compact binaries through second order in the mass ratio
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Two-timescale evolution of extreme-mass-ratio inspirals: waveform generation scheme for quasicircular orbits in Schwarzschild spacetime
• Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits
• The Poincaré and BMS flux-balance laws with application to binary systems
• Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order
• The Overlap of Numerical Relativity, Perturbation Theory and Post-Newtonian Theory in the Binary Black Hole Problem
• High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations
• Gravitational Self-Force Correction to the Innermost Stable Circular Equatorial Orbit of a Kerr Black Hole
• Nonlinear gravitational self-force: second-order equation of motion
• A Surrogate Model for Gravitational Wave Signals from Comparable- to Large- Mass-Ratio Black Hole Binaries
• Analytical high-order post-Newtonian expansions for extreme mass ratio binaries
• Metric perturbations produced by eccentric equatorial orbits around a Kerr black hole
• The adiabatic evolution of orbital parameters in the Kerr spacetime
• Small mass plunging into a Kerr black hole: Anatomy of the inspiral-merger-ringdown waveforms
• Gravitational-Wave Phasing of Quasi-Circular Compact Binary Systems to the Fourth-and-a-Half post-Newtonian Order
• Gravitational radiation from inspiralling compact objects: Spin effects to fourth Post-Newtonian order
• Mechanics of extended masses in general relativity
• Comparing second-order gravitational self-force, numerical relativity and effective one body waveforms from inspiralling, quasi-circular and nonspinning black hole binaries
• Gravitational radiation reaction and second order perturbation theory
• Fast Self-forced Inspirals
• Emergence of Calabi-Yau manifolds in high-precision black hole scattering
• Self-force corrections to the periapsis advance around a spinning black hole
• First Law of Mechanics for Compact Binaries on Eccentric Orbits
• Completion of metric reconstruction for a particle orbiting a Kerr black hole
• Hamilton-Jacobi equation for spinning particles near black holes
• Self-force via $m$-mode regularization and 2+1D evolution: III. Gravitational field on Schwarzschild spacetime
• First Law of Mechanics for Black Hole Binaries with Spins
• Motion of small objects in curved spacetimes: An introduction to gravitational self-force
• Comparison Between Self-Force and Post-Newtonian Dynamics: Beyond Circular Orbits
• From Boundary Data to Bound States III: Radiative Effects
• Confirming and improving post-Newtonian and effective-one-body results from self-force computations along eccentric orbits around a Schwarzschild black hole
• Hamiltonian Formulation of the Conservative Self-Force Dynamics in the Kerr Geometry
• Homoclinic Orbits around Spinning Black Holes II: The Phase Space Portrait
• Quasi-circular inspirals and plunges from non-spinning effective-one-body Hamiltonians with gravitational self-force information
• Waveform Modelling for the Laser Interferometer Space Antenna
• Hamiltonians and canonical coordinates for spinning particles in curved space-time
• Towards a gravitational self force-informed effective-one-body waveform model for nonprecessing, eccentric, large-mass-ratio inspirals
• Second-order gravitational self-force in a highly regular gauge
• New gravitational self-force analytical results for eccentric orbits around a Schwarzschild black hole
• Isofrequency pairing of geodesic orbits in Kerr geometry
• Extreme mass-ratio inspiral and waveforms for a spinning body into a Kerr black hole via osculating geodesics and near-identity transformations
• Gravitational perturbations of rotating black holes in Lorenz gauge
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails
• The mass and angular momentum of reconstructed metric perturbations
• High post-Newtonian order gravitational self-force analytical results for eccentric orbits around a Kerr black hole
• Gauge and motion in perturbation theory
• Numerical computation of the EOB potential q using self-force results
• Complete gravitational-waveform amplitude modes for quasi-circular compact binaries to the 3.5PN order
• Boundary to bound dictionary for generic Kerr orbits
• ESIGMAHM: An Eccentric, Spinning inspiral-merger-ringdown waveform model with Higher Modes for the detection and characterization of binary black holes
• Gravitational Bound Waveforms from Amplitudes
• The top-quark window on compositeness at future lepton colliders
• Spinning particles near Kerr black holes: Orbits and gravitational-wave fluxes through the Hamilton-Jacobi formalism
• Pole N-flation
• Black hole scattering near the transition to plunge: Self-force and resummation of post-Minkowskian theory
• Metric perturbations of Kerr spacetime in Lorenz gauge: Circular equatorial orbits
• Thermodynamics of a Black Hole with Moon
• New self-force method via elliptic partial differential equations for Kerr inspiral models
• Applying the effective-source approach to frequency-domain self-force calculations for eccentric orbits
• Particle motion under the conservative piece of the self-force is Hamiltonian
• A Note on Celestial Mechanics in Kerr Spacetime
• Gravitational memory: new results from post-Newtonian and self-force theory
• Flux-balance laws for spinning bodies under the gravitational self-force
• Post-adiabatic waveform-generation framework for asymmetric precessing binaries
• Actions of spinning compact binaries: Spinning particle in Kerr matched to dynamics at 1.5 post-Newtonian order
• On the integrability of extended test body dynamics around black holes
• Multi-domain spectral method for self-force calculations
• Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order
• Approach to the separatrix with eccentric orbits
• Symplectic mechanics of relativistic spinning compact bodies II.: Canonical formalism in the Schwarzschild spacetime
• Sourced metric perturbations of Kerr spacetime in Lorenz gauge
• High-order post-Newtonian expansion of the generalized redshift invariant for eccentric-orbit, equatorial extreme-mass-ratio inspirals with a spinning primary
• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Simple, efficient method of calculating the Detweiler-Whiting singular field to very high order
• Toward Second-Order Self-Force for Eccentric Extreme-Mass Ratio Inspirals in Schwarzschild Spacetime
• First Law of Mechanics for Spinning Compact Binaries: Dipolar Order
• The first law of binary black hole scattering
• Relieving scale disparity in binary black hole simulations
• Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime
• Comparison of 4.5PN and 2SF gravitational energy fluxes from quasicircular compact binaries
• Constants of motion and fundamental frequencies for elliptic orbits at fourth post-Newtonian order

Cited by in corpus (1)

• Secular evolution of orbital parameters for general bound orbits in Kerr spacetime