Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries

Abstract

Hamiltonian formalisms provide powerful tools for the computation of approximate analytic solutions of the Einstein field equations. The post-Newtonian computations of the explicit analytic dynamics and motion of compact binaries are discussed within the most often applied Arnowitt-Deser-Misner formalism. The obtention of autonomous Hamiltonians is achieved by the transition to Routhians. Order reduction of higher derivative Hamiltonians results in standard Hamiltonians. Tetrad representation of general relativity is introduced for the tackling of compact binaries with spinning components. Compact objects are modeled by use of Dirac delta functions and their derivatives. Consistency is achieved through transition to $d$-dimensional space and application of dimensional regularization. At the fourth post-Newtonian level, tail contributions to the binding energy show up for the first time. The conservative dynamics of binary systems finds explicit presentation and discussion through the fifth post-Newtonian order for spinless masses. For masses with spin Hamiltonians are known through (next-to)${}^3$-leading-order spin-orbit and spin-spin couplings as well as through next-to-leading order cubic and quartic in spin interactions. Parts of those are given explicitly. Tidal-interaction Hamiltonians are considered through (next-to)${}^2$-leading post-Newtonian order. The radiation reaction dynamics is presented explicitly through the third-and-half post-Newtonian order for spinless objects, and, for spinning bodies, to leading-order in the spin-orbit and spin1-spin2 couplings. The most important historical issues get pointed out.

Major revision of G.Schäfer & P.Jaranowski, Living Rev Relativ 21, 7 (2018). Generally updated and improved. New Sections 6.3.3-6.3.5 on results at 5PN to 6PN order. New Section 8 on tidal interactions. Added or updated 65 references. This version is identical to G.Schäfer & P.Jaranowski, Living Rev Relativ 27, 2 (2024)

References in corpus (78)

• Relativistic theory of tidal Love numbers
• Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
• From Scattering Amplitudes to Classical Potentials in the Post-Minkowskian Expansion
• Gravitational scattering, post-Minkowskian approximation and Effective One-Body theory
• High-energy gravitational scattering and the general relativistic two-body problem
• Higher-order spin effects in the dynamics of compact binaries I. Equations of motion
• Dynamical Tides in General Relativity: Effective Action and Effective-One-Body Hamiltonian
• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• Classical and quantum scattering in post-Minkowskian gravity
• 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
• Scattering Amplitudes, the Tail Effect, and Conservative Binary Dynamics at $O(G^4)$
• Dynamics of Binary Systems to Fourth Post-Minkowskian Order from the Effective Field Theory Approach
• Fourth post-Newtonian effective one-body dynamics
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• The Hyperfine Einstein-Infeld-Hoffmann Potential
• Next-to-next-to-leading order spin-orbit effects in the near-zone metric and precession equations of compact binaries
• Novel approach to binary dynamics: application to the fifth post-Newtonian level
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Conservative Tidal Effects in Compact Binary Systems to Next-to-Leading Post-Minkowskian Order
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Effective field theory calculation of second post-Newtonian binary dynamics
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Tidal Effects in the Post-Minkowskian Expansion
• Next-to-leading order gravitational spin-orbit coupling in an effective field theory approach
• Sixth post-Newtonian nonlocal-in-time dynamics of binary systems
• Static two-body potential at fifth post-Newtonian order
• Cubic order spin effects in the dynamics and gravitational wave energy flux of compact object binaries
• Relativistic Closed-Form Hamiltonian for Many-Body Gravitating Systems in the Post-Minkowskian Approximation
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Radiative contributions to gravitational scattering
• ADM canonical formalism for gravitating spinning objects
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Leading order finite size effects with spins for inspiralling compact binaries
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• Binary Dynamics Through the Fifth Power of Spin at $\mathcal{O}(G^2)$
• Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order
• Gravitational scattering of two black holes at the fourth post-Newtonian approximation
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Gravitational spin-orbit coupling in binary systems at the second post-Minkowskian approximation
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Higher-order-in-spin interaction Hamiltonians for binary black holes from Poincaré invariance
• Towers of Gravitational Theories
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics
• Gravitational spin-orbit and aligned spin${}_1$-spin${}_2$ couplings through third-subleading post-Newtonian orders
• Gravitational-wave tail effects to quartic non-linear order
• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• Tidal effects in the equations of motion of compact binary systems to next-to-next-to-leading post-Newtonian order
• The current-type quadrupole moment and gravitational-wave mode $(\ell ,m)=(2,1)$ of compact binary systems at the third post-Newtonian order
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Three-body equations of motion in successive post-Newtonian approximations
• Gravitational Spin-Orbit Hamiltonian at NNNLO in the post-Newtonian framework
• Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. IV. Radiation reaction for binary systems with spin-spin coupling
• Tail contributions to gravitational conservative dynamics
• Completing the Fifth PN Precision Frontier via the EFT of Spinning Gravitating Objects
• N${}^3$LO Quadratic-in-Spin Interactions for Generic Compact Binaries
• N${}^3$LO Spin-Orbit Interaction via the EFT of Spinning Gravitating Objects
• Gravitational Quadratic-in-Spin Hamiltonian at NNNLO in the post-Newtonian framework
• Renormalizing Love: tidal effects at the third post-Newtonian order
• Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling
• Comment on recent papers regarding next-to-leading order spin-spin effects in gravitational interaction
• Hamiltonian for tidal interactions in compact binary systems to next-to-next-to-leading post-Newtonian order
• Gravitational radiation contributions to the two-body scattering angle
• From the EFT of Spinning Gravitating Objects to Poincaré and Gauge Invariance at the 4.5PN Precision Frontier
• Radiation Reaction for Non-Spinning Bodies at 4.5PN in the Effective Field Theory Approach
• Conservative (failed)-tail effects at the fifth post-Newtonian order
• Binary black hole evolutions of approximate puncture initial data
• Binary spinning black hole Hamiltonian in canonical center-of-mass and rest-frame coordinates through higher post-Newtonian order
• Canonical center and relative coordinates for compact binary systems through second post-Newtonian order
• Binary Black Hole Coalescence in Semi-Analytic Puncture Evolution

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• Conservative Dynamics of Binary Systems to Third Post-Minkowskian Order from the Effective Field Theory Approach
• Effective Field Theories of Post-Newtonian Gravity: A comprehensive review
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• Classical Gravitational Bremsstrahlung from a Worldline Quantum Field Theory
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
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• Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order
• Novel approach to binary dynamics: application to the fifth post-Newtonian level
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• GW190521 as a dynamical capture of two nonspinning black holes
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Leading Nonlinear Tidal Effects and Scattering Amplitudes
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• Five-Loop Static Contribution to the Gravitational Interaction Potential of Two Point Masses
• Testing binary dynamics in gravity at the sixth post-Newtonian level
• The Sub-Leading Scattering Waveform from Amplitudes
• The fifth-order post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach: potential contributions
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Enhancing the SEOBNRv5 effective-one-body waveform model with second-order gravitational self-force fluxes
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• The 6th Post-Newtonian Potential Terms at $O(G_N^4)$
• The SXS Collaboration's third catalog of binary black hole simulations
• Generalized quasi-Keplerian solution for eccentric, non-spinning compact binaries at 4PN order and the associated IMR waveform
• Improved gravitational radiation time-scales: significance for LISA and LIGO-Virgo sources
• Comparing Effective One Body Hamiltonians for spin-aligned coalescing binaries
• First post-Newtonian $N$-body problem in Einstein-Cartan theory with the Weyssenhoff fluid: Lagrangian and first integrals
• Inspiral-merger-ringdown waveforms in Einstein-scalar-Gauss-Bonnet gravity within the effective-one-body formalism
• Improved gravitational radiation time-scales II: spin-orbit contributions and environmental perturbations
• Bootstrapping Newton Gravity
• Prospects of detecting deviations to Kerr geometry with radiation reaction effects in EMRIs
• Scattering and dynamical capture of two black holes: synergies between numerical and analytical methods
• Searching for General Binary Inspirals with Gravitational Waves
• Observables from classical black hole scattering in Scalar-Tensor theory of gravity from worldline quantum field theory
• Post-Newtonian templates for gravitational waves from compact binary inspirals
• Mori-Zwanzig formalism for general relativity: a new approach to the averaging problem
• New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: redshift invariant
• New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: gyroscope precession
• Gravitational radiation from inspiralling compact binaries to N${}^3$LO in the Effective Field Theory approach
• Towards a unitary, renormalizable and ultraviolet-complete quantum theory of gravity
• Detweiler's redshift invariant for extended bodies orbiting a Schwarzschild black hole
• Eccentricity estimation from initial data for Numerical Relativity Simulations
• Bootstrapping spinning two body problem in dynamical Chern-Simons gravity using worldline QFT
• Motion of a spinning particle under the conservative piece of the self-force is Hamiltonian to first order in mass and spin
• Second MAYA Catalog of Binary Black Hole Numerical Relativity Waveforms
• Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order
• Modeling matter(s) in SEOBNRv5THM: Generating fast and accurate effective-one-body waveforms for spin-aligned binary neutron stars
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• Post-Newtonian Description of Quantum Systems in Gravitational Fields
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• The Radial Action from Probe Amplitudes to All Orders
• Scattering Amplitudes for Binary Systems beyond GR
• Three models of non-perturbative quantum-gravitational binding
• Quantum point particle approximation of spinning black holes and compact stars