Numerical computation of the effective-one-body potential q using self-force results

Abstract

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 nonspinning compact objects in the extreme mass-ratio limit is given in terms of three potentials: a(v), d¯(v), q(v). By generalizing the first law of mechanics for (nonspinning) black hole binaries to eccentric orbits, [A. Le Tiec, Phys. Rev. D 92, 084021 (2015).] recently obtained new expressions for 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?v?1/6. Our computation thus provides the first-ever strong-field results for q(v). We also obtain d¯(v) in our entire domain to a fractional accuracy of ?10-8. We find that our results are compatible with the known post-Newtonian expansions for d¯(v) and q(v) in the weak field, and agree with previous (less accurate) numerical results for d¯(v) in the strong field.

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