Gravitational spin-orbit and aligned <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>spin</mml:mi></mml:mrow><mml:mrow><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mtext>−</mml:mtext><mml:msub><mml:mrow><mml:mi>spin</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> couplings through third-subleading post-Newtonian orders
Andrea Antonelli, Chris Kavanagh, Mohammed Khalil, Jan Steinhoff, Justin Vines
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) ${\mathrm{spin}}_{1}\text{\ensuremath{-}}{\mathrm{spin}}_{2}$ 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.