Gravitational spin-orbit coupling through the third-subleading post-Newtonian order: Exploring spin-gauge flexibility

We build upon recent work by Antonelli et al. [Gravitational spin-orbit coupling through third-subleading post-Newtonian order: From first-order self-force to arbitrary mass ratios, Phys. Rev. Lett. 125, 011103 (2020).] to obtain, within the effective-one-body formalism, and for an arbitrary choice of gauge, the third-subleading post-Newtonian (4.5PN) corrections to the spin-orbit conservative dynamics of spin-aligned binaries. This is then specialized to (i) the well-known Damour-Jaranowski-Schäfer (DJS) gauge, where the dependence on the angular momentum of the gyrogravitomagnetic functions $(G_S,G_{S_{*}})$ is removed and (ii) to an alternative gauge (called anti-DJS gauge, $\overline{\mathrm{DJS}}$) that is chosen so as to precisely reproduce the Hamiltonian of a spinning test particle at linear order in the particle spin and keep the full dependence on the radial and angular momentum in $(G_S,G_{S_{*}})$. We use these results to extend by one perturbative order, in post-Newtonian sense, the analytical knowledge of the periastron advance. After performing a suitable factorization and resummation of $(G_S,G_{S_{*}})$, the DJS and $\overline{\mathrm{DJS}}$ performances are compared via various gauge-invariant quantities at the effective-one-body last stable circular orbit. We eventually find some indications that the $\overline{\mathrm{DJS}}$ gauge might be advantageous in the description of the inspiral dynamics of circularized binaries.

Figure 1

Binding energy at the LSO versus ${\tilde{a}}_0$ in the equal-mass, equal-spin case. Top panel: comparison between the binding energy of the EOB model teobresums with its NR-calibrated spin-orbit sector (blue dashed line) to different ${\mathrm{N}}^3\mathrm{LO}$-accurate prescriptions of the gyrogravitomagnetic functions: (i) DJS gauge (green line), (ii) Kerr-factorized $\overline{\mathrm{DJS}}$ gauge functions (red line), and (iii) EOB-factorized $\overline{\mathrm{DJS}}$ gauge (purple line). Each curve stops at the value of ${\tilde{a}}_0$ for which the LSO no longer exists. Bottom panel: binding energy difference between the various ${\mathrm{N}}^3\mathrm{LO}$ curves and the corresponding NR-calibrated teobresums value.

Figure 2

Analog of Fig. 1 for the Kerr parameter ${\chi }_J$ at the LSO. We also add the numerical result of Ref. [53] (dash-dotted black line), which represents the Kerr parameter of the residual BH after the coalescence. The loss of angular momentum between the LSO and merger is responsible for the lower values of this quantity.