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

2025/04/17 by Trestini, David · 13 citations
#FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.2504.13245

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 (ℓ,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.

Citations

• Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework
• Approximate helical symmetry in compact binaries
• Effective-one-body waveform model for noncircularized, planar, coalescing black hole binaries II:high accuracy by improving logarithmic terms in resummations
• Comparison of 4.5PN and 2SF gravitational energy fluxes from quasicircular compact binaries
• Effective-one-body waveform model for non-circularized, planar, coalescing black hole binaries: the importance of radiation reaction
• The current-type quadrupole moment and gravitational-wave mode (ℓ,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
• Fourth post-Newtonian Hamiltonian dynamics of two-body systems from an effective field theory approach
• Second-order self-force calculation of the gravitational binding energy in compact binaries
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach II: Renormalized Lagrangian
• Conservative dynamics of binary systems to fourth Post-Newtonian order in the EFT approach I: Regularized Lagrangian
• Flux-balance equations for linear momentum and center-of-mass position of self-gravitating post-Newtonian systems
• Center-of-Mass Equations of Motion and Conserved Integrals of Compact Binary Systems at 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
• First Law of Compact Binary Mechanics with Gravitational-Wave Tails
• Effective field theory approach to the gravitational two-body dynamics, at fourth post-Newtonian order and quintic in the Newton constant
• Energy and periastron advance of compact binaries on circular orbits at the fourth post-Newtonian order
• Masses, Radii, and the Equation of State of Neutron Stars
• Conservative dynamics of two-body systems at the fourth post-Newtonian approximation of general relativity
• Fokker action of non-spinning compact binaries at the fourth post-Newtonian approximation
• The tail effect in gravitational radiation-reaction: time non-locality and renormalization group evolution
• Derivation of local-in-time fourth post-Newtonian ADM Hamiltonian for spinless compact binaries
• Fourth post-Newtonian effective one-body dynamics
• Nonlocal-in-time action for the fourth post-Newtonian conservative dynamics of two-body systems
• Post-Newtonian Theory for Gravitational Waves
• Analytical determination of the two-body gravitational interaction potential at the 4th post-Newtonian approximation
• Horizon-absorbed energy flux in circularized, nonspinning black-hole binaries and its effective-one-body representation
• Tail terms in gravitational radiation reaction via effective field theory
• First law of binary black hole mechanics in general relativity and post-Newtonian theory
• 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
• Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit
• Nonrotating black hole in a post-Newtonian tidal environment
• Perspective on gravitational self-force analyses
• Gravitational radiation reaction in the equations of motion of compact binaries to 3.5 post-Newtonian order
• Binary black-hole dynamics at the third-and-a-half post-Newtonian order in the ADM formalism
• 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
• A General Definition of "Conserved Quantities" in General Relativity and Other Theories of Gravity
• Second post-Newtonian gravitational radiation reaction for two-body systems: Nonspinning bodies
• Gravitational radiation reaction and balance equations to post-Newtonian order
• Gravitational radiation from compact binary systems: gravitational waveforms and energy loss to second post-Newtonian order
• Hereditary effects in gravitational radiation
• Radiative gravitational fields in general relativity I. General structure of the field outside the source
• Multipole expansions of gravitational radiation
• The 2.5PN gravitational wave polarisations from inspiralling compact binaries in circular orbits

Cited by

• Post-adiabatic self-force waveforms: slowly spinning primary and precessing secondary
• Spin-aligned inspiral waveforms from self-force and post-Newtonian theory
• Hybrid waveform model for asymmetric spinning binaries: Self-force meets post-Newtonian theory
• General Fourier expansion of post-Newtonian binary dynamics based on a quasi-Keplerian framework
• Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime
• Post-adiabatic dynamics and waveform generation in self-force theory: an invariant pseudo-Hamiltonian framework
• Tidal effects in gravitational and scalar waveforms and fluxes to one post-Newtonian order in massless scalar-tensor theories
• Constants of motion in gravitational self-force theory

Related

• Binding energy of compact stars and their non-radial oscillations
• Conservative Dynamics of Binary Systems of Compact Objects at the Fourth Post-Newtonian Order
• Gravitational waves from quasielliptic compact binaries in scalar-tensor theory to one-and-a-half post-Newtonian order
• Innermost stable circular orbit of arbitrary-mass compact binaries at fourth post-Newtonian order
• Half-integral conservative post-Newtonian approximations in the redshift factor of black hole binaries