Abstract
The study of scattering encounters continues to provide new insights into the general relativistic two-body problem. The local-in-time conservative dynamics of an aligned-spin binary, for both unbound and bound orbits, is fully encoded in the gauge-invariant scattering-angle function, which is most naturally expressed in a post-Minkowskian (PM) expansion, and which exhibits a remarkably simple dependence on the masses of the two bodies (in terms of appropriate geometric variables). This dependence links the PM and small-mass-ratio approximations, allowing gravitational self-force results to determine new post-Newtonian (PN) information to all orders in the mass ratio. In this paper, we exploit this interplay between relativistic scattering and self-force theory to obtain the third-subleading (4.5PN) spin-orbit dynamics for generic spins, and the third-subleading (5PN) spin$_1$-spin$_2$ dynamics for aligned spins. We further implement these novel PN results in an effective-one-body framework, and demonstrate the improvement in accuracy by comparing against numerical-relativity simulations.
Highlights
The burgeoning field of gravitational-wave (GW) astronomy has already shown its potential to revolutionize our understanding of our universe [1], gravity [2], and the nature of compact objects [3,4], such as black holes (BHs) and neutron stars
Our derivations are organized in the following procedure: (1) We argue that the scattering angle for an alignedspin binary has a simple dependence on the masses, which extends the result of Ref. [100] for nonspinning binaries
GW astronomy allows a multitude of applications in fundamental and astrophysics [1,2,3,4] that rely on accurate waveform models for inferring the source parameters
Summary
The burgeoning field of gravitational-wave (GW) astronomy has already shown its potential to revolutionize our understanding of our universe [1], gravity [2], and the nature of compact objects [3,4], such as black holes (BHs) and neutron stars. Several other works have considered amplitudes methods in relation to spinning two-body systems, beyond the SO and S1S2 sectors (beyond the dipole level in the bodies’ multipole expansions), in particular for special cases such as bodies with black-holelike spin-induced multipole structure and/or for the alignedspin configuration (in which the bodies’ spins are [anti-] parallel to the orbital angular momentum); see, e.g., [45,98,99] and references reviewed therein These works demonstrate that the study of gravitational scattering continues to provide novel results and useful insights on the relativistic two-body problem, with implications for precision gravitational-wave astronomy yet to be explored. GSF results available in the literature to determine the remaining coefficients of the scattering angle Vital to this step is the first law of spinning binary mechanics [58,103,104], which is used to relate the radial action to the redshift and precession frequency, and for which we discuss an extension to arbitrary-mass-ratio aligned-spin eccentric orbits. Appendix A contains expressions for tail terms in the radial action, while Appendix B contains explicit expressions for a certain mapping between variables used to connect redshift and precession-invariant results from the radial action to GSF results in the literature, which have been previously erroneously (yet innocuously) reported in the literature
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
