论文标题
二进制黑洞模拟中的红移因子和小质量比率极限
Redshift factor and the small mass-ratio limit in binary black hole simulations
论文作者
论文摘要
我们根据二进制黑洞模拟中的Detweiler红移因子的计算基于其与表面重力的关系。红移因子在分析近似，重力自力计算和保守的两体动力学中具有深远的应用。通过专门研究非旋转，质量比的准圆形二进制文件从$ m_a/m_b = 1 $到$ m_a/m_b = 9.5 $，我们能够单独从模拟中恢复$ 10^{ - 5} $的相对差异的领先小型质量（SMR）预测。我们提取的次要订单术语与自力计算产生的SMR预测一致，差异为几％。这些与一阶保守预测的偏差与可以在SMR扩展中适应的非绝热效应一致。这一事实也得到了与保守的纽顿后红移预测的比较。对于各个红移，根据对称质量比$ν$的重新扩张并不能改善该系列的收敛性。但是，我们发现，当查看两个后孔的红移因子的总和时，$ z_a + z_b $，在群众交换下是对称的，$ν$的重新扩张会加速其收敛性。我们的工作提供了进一步的证据，表明SMR近似值在建模甚至可比的质量二进制黑洞中具有令人惊讶的有效性。
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 $ν$ 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 $ν$ accelerates its convergence. Our work provides further evidence of the surprising effectiveness of SMR approximations in modeling even comparable mass binary black holes.
