Redshift factor and the small mass-ratio limit in binary black hole simulations
Redshift factor and the small mass-ratio limit in binary black hole simulations
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DOI：
10.1103/physrevd.106.044006
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发表时间：
2022-03
影响因子：
5
通讯作者：
Sergi Navarro Albalat;A. Zimmerman;M. Giesler;M. Scheel
中科院分区：
文献类型：
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作者：
Sergi Navarro Albalat;A. Zimmerman;M. Giesler;M. Scheel
基于双黑洞表面重力的关系，给出了双黑洞模拟中德魏勒红移因子的计算方法。红移因子在解析近似、引力自力计算和保守二体动力学中有着深远的应用。通过专门研究质量比在$m_A/m_B = 1$到$m_A/m_B = 9.5$之间的非旋转准圆双星，我们能够从单独的模拟中恢复相对差为$10^{-5}$的领先小质量比（SMR）预测。我们提取的次领先阶项与自力计算产生的SMR预测一致，差异为几个百分点。这些与一阶保守预测的偏差与SMR膨胀中可以容纳的非绝热效应相一致。这一事实也得到了与保守的后牛顿预测红移的比较的支持。对于单个红移，根据对称质量比$\nu$的重新展开并不能改善级数的收敛性。然而，我们发现，当观察两个后洞的红移因子和时，$z_A + z_B$，它在质量交换下是对称的，$\nu$中的再膨胀加速了它的收敛。我们的工作进一步证明了SMR近似在模拟质量相当的双黑洞时惊人的有效性。
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 $m_A/m_B = 1$ to $m_A/m_B = 9.5$ we are able to recover the leading small-mass-ratio (SMR) prediction with relative differences of order $10^{-5}$ 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 $\nu$ 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, $z_A + z_B$, which is symmetric under the exchange of the masses, a re-expansion in $\nu$ accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.