List of Figures
The binding energy versus in the equal-mass case (). Left panel: Comparison with the numerical relativity result of Gourgoulhon, Grandclément et al. [228, 232] valid in the corotating case (marked by a star). Points indicated by are computed from the minimum of Eq. (232), and correspond to irrotational binaries. Points denoted by come from the minimum of the sum of Eqs. (232) and (250*), and describe corotational binaries. Note the very good convergence of the standard (Taylor-expanded) PN series. Right panel: Numerical relativity results of Cook, Pfeiffer et al. [133, 121] for quasi-equilibrium (QE) configurations and various boundary conditions for the lapse function, in the non-spinning (NS), leading-order non spinning (LN) and corotating (CO) cases. The point from [228, 232] (HKV-GGB) is also reported as in the left panel, together with IVP, the initial value approach with effective potential [132, 342], as well as standard PN predictions from the left panel and non-standard (EOB) ones. The agreement between the QE computation and the standard non-resummed 3PN point is excellent especially in the irrotational NS case.
Different analytical approximation schemes and numerical techniques to study black hole binaries, depending on the mass ratio and the post-Newtonian parameter . Post-Newtonian theory and perturbative self-force analysis can be compared in the post-Newtonian regime ( thus ) of an extreme mass ratio () binary.
Variation of the enhancement factor with the eccentricity . This function agrees with the numerical calculation of Ref.  modulo a trivial rescaling with the Peters–Mathews function (356a). The inset graph is a zoom of the function at a smaller scale. The dots represent the numerical computation and the solid line is a fit to the numerical points. In the circular orbit limit we have .
Geometric definitions for the precessional motion of spinning compact binaries [54, 306]. We show (i) the source frame defined by the fixed orthonormal basis ; (ii) the instantaneous orbital plane which is described by the orthonormal basis ; (iii) the moving triad and the associated three Euler angles , and ; (v) the direction of the total angular momentum which coincides with the –direction. Dashed lines show projections into the – plane.