Equations of motion for compact binary systems in general relativity: Do they depend on the bodies' internal structure at the third post-Newtonian order?
arXiv:2503.03189 · doi:10.1103/PhysRevD.111.104034
Abstract
We present and discuss the possibility, derived from work carried out 20 years ago, that the equations of motion for compact binary neutron stars at the third post-Newtonian (3PN) order in general relativity might actually depend on the internal structure of the bodies. These effects involve integrals over the density and internal gravitational potentials of the bodies that are independent of the mass and radius of the bodies, but dependent on their equations of state. These effects could alter the coefficients in the 3PN equations derived using ``point mass'' methods by as much as 100 percent. They were found in independent calculations done at Washington University using the Direct Integration of the Relaxed Einstein Equations (DIRE) approach, and at the Institut d'Astrophysique de Paris using the Multipolar post-Minkowskian (MPPM) approach. Neither calculation was completed because of the enormous complexity of the algebraic computations and the limitations of software of the day (Maple, Mathematica), and because of an assumption that the effects would somehow cancel or be removable by some transformation. This assumption was rooted in the Strong Equivalence Principle (SEP), which would suppress such effects up to the stage where tidal interactions become important, effectively 5PN order for compact bodies. SEP was well supported at lower PN orders and in special examples. We argue that this assumption needs to be verified by calculations. If the results show that these terms exactly cancel or can be absorbed into renormalized masses or shifted positions of each body, this would provide support for the Strong Equivalence Principle. But if they do not cancel and are not incorporated into gravitational waveforms, they could impact efforts using next-generation gravitational-wave interferometers to extract information about the equation of state for neutron star matter.
14 pages, minor changes to align with published version
References in corpus (18)
- GW170817: Observation of Gravitational Waves from a Binary Neutron Star Inspiral
- GWTC-3: Compact Binary Coalescences Observed by LIGO and Virgo During the Second Part of the Third Observing Run
- The NANOGrav 15-year Data Set: Evidence for a Gravitational-Wave Background
- Science Case for the Einstein Telescope
- The MICROSCOPE mission: first results of a space test of the Equivalence Principle
- A millisecond pulsar in a stellar triple system
- Neutron star tidal deformability and equation of state constraints
- Post-Newtonian Gravitational Radiation and Equations of Motion via Direct Integration of the Relaxed Einstein Equations. I. Foundations
- 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
- New derivation of a third post-Newtonian equation of motion for relativistic compact binaries without ambiguity
- The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part
- Effective field theory calculation of conservative binary dynamics at third post-Newtonian order
- Probing Fundamental Physics with Gravitational Waves: The Next Generation
- Equation of motion for relativistic compact binaries with the strong field point particle limit: Third post-Newtonian order
- Equation of motion for relativistic compact binaries with the strong field point particle limit : Formulation, the first post-Newtonian and multipole terms
- 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
- Post-Newtonian gravitational radiation and equations of motion via direct integration of the relaxed Einstein equations. V. Evidence for the strong equivalence principle to second post-Newtonian order
- Application of energy and angular momentum balance to gravitational radiation reaction for binary systems with spin-orbit coupling