Schott term in the binding energy for compact binaries on circular orbits at fourth post-Newtonian order

Abstract

The phasing for compact binary systems on circular orbits was obtained in arXiv:2304.11185 at fourth-and-a-half post-Newtonian (4.5PN) order thanks to two main ingredients: the 4PN conservative energy (associated to a nonradiative spacetime) in terms of the orbital frequency and the 4.5PN flux in terms of the waveform frequency (i.e., the half-frequency of the $(\ell ,m)=(2,2)$ mode). When obtaining the phasing, a key physical postulate was made: the expression of the binding energy in terms of the waveform frequency was assumed to be identical to the expression of the conservative energy in terms of the orbital frequency. This postulate was necessary to ensure that the frequency evolution obtained through the flux-balance law (which involves the binding energy) was independent of the choice of spacetime foliation. In this work, I show that the binding energy entering the flux-balance law differs from the 4PN conservative energy by a 4PN pseudo-Schott term, associated with radiation-reaction effects due to gravitational tails. Unlike the usual Schott terms (at 2.5PN, 3.5PN and 4.5PN), the pseudo-Schott term is not a total derivative and is in fact hereditary, so it does not vanish for circular orbits. Remarkably, the binding energy thus obtained is in perfect agreement with the one obtained using the aforementioned physical postulate, which confirms that the 4.5PN phasing associated to the waveform frequency computed in arXiv:2304.11185 is indeed correct. This result is extended to the other Poincaré invariants, and `thermodynamic' relations between the binding energy and angular momentum are established. Finally, the chirp and phasing associated to the orbital frequency are presented at 4.5PN, including horizon-absorption effects.

21 pages. v2: title update and minor corrections (matches published version)

References in corpus (47)

• Masses, Radii, and Equation of State of Neutron Stars
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Topological Black Holes in Horava-Lifshitz Gravity
• 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
• Fourth post-Newtonian effective one-body dynamics
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits
• Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
• The First Law of Binary Black Hole Mechanics in General Relativity and Post-Newtonian Theory
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• 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
• Energy and periastron advance of compact binaries on circular orbits 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
• Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Nonrotating black hole in a post-Newtonian tidal environment
• Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at the Fourth Post-Newtonian Order
• The binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM-formalism
• Perspective on gravitational self-force analyses
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Tail terms in gravitational radiation reaction via effective field theory
• Gravitational-Wave Phasing of Quasi-Circular Compact Binary Systems to the Fourth-and-a-Half post-Newtonian Order
• Gravitational Wave Flux and Quadrupole Modes from Quasi-Circular Non-Spinning Compact Binaries to the Fourth Post-Newtonian Order
• Dimensional regularization of the IR divergences in the Fokker action of point-particle binaries at the fourth post-Newtonian order
• Spherical harmonic modes of 5.5 post-Newtonian gravitational wave polarizations and associated factorized resummed waveforms for a particle in circular orbit around a Schwarzschild black hol
• The current-type quadrupole moment and gravitational-wave mode $(\ell ,m)=(2,1)$ of compact binary systems at the third post-Newtonian order
• The mass quadrupole moment of compact binary systems at the fourth post-Newtonian order
• Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation
• Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems
• The Wald-Zoupas prescription for asymptotic charges at null infinity in general relativity
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails
• Gravitational-wave tails of memory
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: From Source to Canonical Moment
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: II. Dimensional Regularization and Renormalization
• Investigating tidal heating in neutron stars via gravitational Raman scattering
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: Relating the Harmonic and Radiative Metrics
• The Quadrupole Moment of Compact Binaries to the Fourth post-Newtonian Order: I. Non-Locality in Time and Infra-Red Divergencies
• Radiation Reaction for Non-Spinning Bodies at 4.5PN in the Effective Field Theory Approach
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order
• Gravitational radiation from inspiralling compact binaries to N${}^3$LO in the Effective Field Theory approach
• Spectral weight in Chern-Simons theory with symmetry breaking
• Approximate helical symmetry in compact binaries

Cited by in corpus (6)

• Constants of motion in gravitational self-force theory
• Comparison of 4.5PN and 2SF gravitational energy fluxes from quasicircular compact binaries
• Gravitational radiation reaction for compact binary systems at the fourth-and-a-half post-Newtonian order in harmonic coordinates
• General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework
• Tidal effects in the total flux and waveform in massless scalar-tensor theories to, respectively, relative 2PN and 1.5PN orders
• Fixing the center-of-mass frame of numerical relativity waveforms using the post-Newtonian center-of-mass charge