Logarithmic tail contributions to the energy function of circular compact binaries

Abstract

We combine different techniques to extract information about the logarithmic contributions to the two-body conservative dynamics within the post-Newtonian (PN) approximation of General Relativity. The logarithms come from the conservative part of non linear gravitational-wave tails and their iterations. Explicit, original expressions are found for conservative dynamics logarithmic tail terms up to 6PN order by adopting both traditional PN calculations and effective field theory (EFT) methods. We also determine all logarithmic terms at 7PN order, fixing a sub-leading logarithm from a tail-of-tail-of-tail process by comparison with self-force (SF) results. Moreover, we use renormalization group techniques to obtain the leading logarithmic terms to generic power $n$, appearing at $(3n+1)$PN order, and we resum the infinite series in a closed form. Half-integer PN orders enter the conservative dynamics starting at 5.5PN, but they do not generate logarithmic contributions up to next-to-next-to-leading order included. We nevertheless present their contribution at leading order in the small mass ratio limit.

arXiv comment17 pages, 1 figure. 2 paragraphs added to sec. IV A in v2

References in corpus (47)

• An Effective Field Theory of Gravity for Extended Objects
• The Effective Field Theorist's Approach to Gravitational Dynamics
• Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• A consequence of the gravitational self-force for circular orbits of the Schwarzschild geometry
• Gravitational Self Force in a Schwarzschild Background and the Effective One Body Formalism
• Gravitational radiative corrections from effective field theory
• Gravitational waves from inspiralling compact binaries: Energy flux to third post-Newtonian order
• High-Order Post-Newtonian Fit of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Gravitational-wave tails of tails
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Second-post-Newtonian generation of gravitational radiation
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• On the multipole expansion of the gravitational field
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Gravitational Self-Force Correction to the Binding Energy of Compact Binary Systems
• Effective field theory methods to model compact binaries
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Ambiguity-Free Completion of the Equations of Motion of Compact Binary Systems at the Fourth Post-Newtonian Order
• The dynamics of the gravitational two-body problem at fourth post-Newtonian order and at quadratic order in the Newton constant
• Thermodynamics of binary black holes and neutron stars
• Post-Newtonian and Numerical Calculations of the Gravitational Self-Force for Circular Orbits in the Schwarzschild Geometry
• Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits
• 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
• Hadamard regularization of the third post-Newtonian gravitational wave generation of two point masses
• Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order
• High-order post-Newtonian contributions to the two-body gravitational interaction potential from analytical gravitational self-force calculations
• Tail terms in gravitational radiation reaction via effective field theory
• Analytical high-order post-Newtonian expansions for extreme mass ratio binaries
• Canonical Formulation of Spin in General Relativity
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Non-linear multipole interactions and gravitational-wave octupole modes for inspiralling compact binaries to third-and-a-half post-Newtonian order
• Finding high-order analytic post-Newtonian parameters from a high-precision numerical self-force calculation
• Equation of motion for relativistic compact binaries with the strong field point particle limit : Formulation, the first post-Newtonian and multipole terms
• Hereditary Terms at Next-To-Leading Order in Two-Body Gravitational Dynamics
• Gravitational-wave tail effects to quartic non-linear order
• Analytic self-force calculations in the post-Newtonian regime: eccentric orbits on a Schwarzschild background
• Black hole mass dynamics and renormalization group evolution
• Detweiler's gauge-invariant redshift variable: analytic determination of the nine and nine-and-a-half post-Newtonian self-force contributions
• Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries
• High-order half-integral conservative post-Newtonian coefficients in the redshift factor of black hole binaries
• On the behavior of causal geodesics on a Kerr-de Sitter spacetime

Cited by in corpus (28)

• Post-Minkowskian Effective Field Theory for Conservative Binary Dynamics
• Scattering Amplitudes and Conservative Binary Dynamics at $\mathcal{O}(G^4)$
• 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
• Conservative Dynamics of Binary Systems at Fourth Post-Minkowskian Order in the Large-eccentricity Expansion
• Gravitational Bremsstrahlung from Reverse Unitarity
• Sixth post-Newtonian local-in-time dynamics of binary systems
• Binary dynamics at the fifth and fifth-and-a-half post-Newtonian orders
• Gravitational Bremsstrahlung in the Post-Minkowskian Effective Field Theory
• Spin Effects in the Effective Field Theory Approach to Post-Minkowskian Conservative Dynamics
• Radiation-Reaction in the Effective Field Theory Approach to Post-Minkowskian Dynamics
• The Science of the Einstein Telescope
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Gravitational radiation from inspiralling compact objects: Spin-spin effects completed at the next-to-leading 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
• Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model
• Eccentric-orbit extreme-mass-ratio-inspiral radiation II: 1PN correction to leading-logarithm and subleading-logarithm flux sequences and the entire perturbative 4PN flux
• Large Gauge Effects and the Structure of Amplitudes
• Gravitational radiation contributions to the two-body scattering angle
• A tale of tails through generalized unitarity
• Gravitational Multipole Renormalization
• Radiative Classical Gravitational Observables at $\mathcal{O}(G^3)$ from Scattering Amplitudes
• Multipole expansion at the level of the action in $d$-dimensions
• Conservative (failed)-tail effects at the fifth post-Newtonian order
• Gravitational radiation from inspiralling compact binaries to N${}^3$LO in the Effective Field Theory approach
• Higher-order tails and RG flows due to scattering of gravitational radiation from binary inspirals