Numerical computation of the EOB potential q using self-force results

The effective-one-body theory (EOB) describes the conservative dynamics of compact binary systems in terms of an effective Hamiltonian approach. The Hamiltonian for moderately eccentric motion of two non-spinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: $a(v), \bar{d}(v), q(v)$. By generalizing the first law of mechanics for (non-spinning) black hole binaries to eccentric orbits, [\prd{\bf92}, 084021 (2015)] recently obtained new expressions for $\bar{d}(v)$ and $q(v)$ in terms of quantities that can be readily computed using the gravitational self-force approach. Using these expressions we present a new computation of the EOB potential $q(v)$ by combining results from two independent numerical self-force codes. We determine $q(v)$ for inverse binary separations in the range $1/1200 \le v \lesssim 1/6$. Our computation thus provides the first-ever strong-field results for $q(v)$. We also obtain $\bar{d}(v)$ in our entire domain to a fractional accuracy of $\gtrsim 10^{-8}$. We find to our results are compatible with the known post-Newtonian expansions for $\bar{d}(v)$ and $q(v)$ in the weak field, and agree with previous (less accurate) numerical results for $\bar{d}(v)$ in the strong field.

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