Fixing the BMS frame of numerical relativity waveforms with BMS charges
Fixing the BMS frame of numerical relativity waveforms with BMS charges
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DOI：
10.1103/physrevd.106.084029
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发表时间：
2022-08
影响因子：
5
通讯作者：
Keefe Mitman;L. Stein;M. Boyle;N. Deppe;François Hébert;Lawrence E. Kidder;Jordan Moxon;M. Scheel;S. Teukolsky;William Throwe;Nils L. Vu
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文献类型：
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作者：
Keefe Mitman;L. Stein;M. Boyle;N. Deppe;François Hébert;Lawrence E. Kidder;Jordan Moxon;M. Scheel;S. Teukolsky;William Throwe;Nils L. Vu
Bondi-van der Burg-Metzner-Sachs （BMS）群独特地描述了渐近无穷大的对称性，从而描述了在那里传播的引力波的对称性，对于波形的精确建模已经变得越来越重要。特别是，波形模型，如后牛顿（PN）表达式、数值相对论（NR）和黑洞摄动理论，产生的结果在不同的BMS框架中。因此，为了建立致密天体合并过程中产生的波形模型，理想情况下是PN、NR和黑洞摄动理论的混合，需要一种快速而稳健的方法来固定BMS自由度。在这项工作中，我们提出了第一种固定NR波形的整个BMS自由度的方法，以匹配PN波形或黑洞摄动理论的框架。我们通过寻找以规定的方式改变某些电荷的BMS变换来实现这一点——例如，找到将质心电荷映射到平均值为零的质心变换。我们发现这种新方法比以前依赖于优化算法的方法要快20倍，并且在映射到超rest帧时更加正确。此外，在开发这种基于电荷的框架固定方法的过程中，我们计算了无自旋和有自旋的Moreschi超动量的PN表达式。这个Moreschi超动量有效地等价于未来零无穷处的能量通量或零内存贡献$\mathscr{I}^{+}$。从这个PN计算中，我们还计算了振荡（$m\not=0$模式）和自旋相关的记忆项，这些记忆项以前没有被识别出来，或者在后牛顿文献中的应变表达式中缺失。
The Bondi-van der Burg-Metzner-Sachs (BMS) group, which uniquely describes the symmetries of asymptotic infinity and therefore of the gravitational waves that propagate there, has become increasingly important for accurate modeling of waveforms. In particular, waveform models, such as post-Newtonian (PN) expressions, numerical relativity (NR), and black hole perturbation theory, produce results that are in different BMS frames. Consequently, to build a model for the waveforms produced during the merging of compact objects, which ideally would be a hybridization of PN, NR, and black hole perturbation theory, one needs a fast and robust method for fixing the BMS freedoms. In this work, we present the first means of fixing the entire BMS freedom of NR waveforms to match the frame of either PN waveforms or black hole perturbation theory. We achieve this by finding the BMS transformations that change certain charges in a prescribed way -- e.g., finding the center-of-mass transformation that maps the center-of-mass charge to a mean of zero. We find that this new method is 20 times faster, and more correct when mapping to the superrest frame, than previous methods that relied on optimization algorithms. Furthermore, in the course of developing this charge-based frame fixing method, we compute the PN expression for the Moreschi supermomentum to 3PN order without spins and 2PN order with spins. This Moreschi supermomentum is effectively equivalent to the energy flux or the null memory contribution at future null infinity $\mathscr{I}^{+}$. From this PN calculation, we also compute oscillatory ($m\not=0$ modes) and spin-dependent memory terms that have not been identified previously or have been missing from strain expressions in the post-Newtonian literature.