Redshift factor and the small mass-ratio limit in binary black hole simulations
arXiv:2203.04893 · doi:10.1103/PhysRevD.106.044006
Abstract
We present a calculation of the Detweiler redshift factor in binary black hole simulations based on its relation to the surface gravity. The redshift factor has far-reaching applications in analytic approximations, gravitational self-force calculations, and conservative two-body dynamics. By specializing to non-spinning, quasi-circular binaries with mass ratios ranging from to we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order from simulations alone. The next-to-leading order term that we extract agrees with the SMR prediction arising from self-force calculations, with differences of a few percent. These deviations from the first-order conservative prediction are consistent with non-adiabatic effects that can be accommodated in an SMR expansion. This fact is also supported by a comparison to the conservative post-Newtonian prediction of the redshifts. For the individual redshifts, a re-expansion in terms of the symmetric mass ratio does not improve the convergence of the series. However we find that when looking at the sum of the redshift factors of both back holes, , which is symmetric under the exchange of the masses, a re-expansion in accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.
arXiv comment22 pages, 23 figures
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