Gravitational Spin-Orbit Coupling through Third-Subleading Post-Newtonian Order: From First-Order Self-Force to Arbitrary Mass Ratios

Exploiting simple yet remarkable properties of relativistic gravitational scattering, we use first-order self-force (linear-in-mass-ratio) results to obtain arbitrary-mass-ratio results for the complete third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit sector of spinning-binary conservative dynamics, for generic (bound or unbound) orbits and spin orientations. We thereby improve important ingredients of models of gravitational waves from spinning binaries, and we demonstrate the improvement in accuracy by comparing against aligned-spin numerical simulations of binary black holes.

Figure 1

Illustration of aligned-spin scattering BHs.

Figure 2

Comparison of the gauge-invariant relation between the circular-orbit aligned-spin spin-orbit binding energy $E_b$ and $v_{\omega }$. The figure shows results obtained numerically from the (PN-resummed) EOB Hamiltonian (2) and NR results from Refs. [83, 84]. The linear-in-spin contribution is isolated using Eq. (11) with spin magnitudes $\widehat{a}=0.6$ and for mass ratios $q=1$ and $1/3$.