Numerical computation of the effective-one-body potentialqusing 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 non-spinning 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 (non-spinning) black hole binaries to eccentric orbits, [A. Le Tiec Phys. Rev. D92, 084021 (2015)] recently obtained new expressions ford(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 obtaind(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 ford(v) and q(v) in the weak field, and agree with previous (less accurate) numerical results ford(v) in the strong field.

Spin–orbit precession for eccentric black hole binaries at first order in the mass ratio

“…(3.8) and (3.10), with the correction term ∆Φ e→0 determined by the EOB ρ function, with ρ constituted from the circular-orbit redshift invariant z and the EOBd function, and with the latter numerically computed to high accuracy in Ref. [66]. The analytic result ∆ψ 9.5 e 0 was described in Sec.…”

Complete waveform model for compact binaries on eccentric orbits

“…[44] at small eccentricity [34]; (vi) hybrid waveforms that describe highly eccentric systems: these waveforms describe the inspiral evolution using geodesic equations of motion, and the merger phase is modeled using a semianalytical prescription that captures the features of NR simulations [51]; (vii) self-force calculations for nonspinning BHs along eccentric orbits [52][53][54][55][56][57][58][59]; and (viii) NR simulations that explore the dynamics of eccentric binary systems [47,[60][61][62][63][64][65][66][67][68][69].…”

Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription

“…Notably, the EOB formalism has provided, through its natural theoretical flexibility, a common ground for incorporating the results of other approaches. Examples of recent works contributing to the crossbreeding between EOB theory and other approximation methods are: EOB PN [9][10][11][12]; EOB PM [13]; EOB SF [14][15][16][17]; and EOB NR [18][19][20][21][22].…”