在使用准Kinnersley四分体的数值相对论模拟中探索时空动力学的几何激发的坐标系
A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad
摘要：
我们调查的适用性和性质的准Kinnersley四分体和几何动机的坐标系作为工具，用于量化强场和波区效应的数值相对论（NR）模拟。我们固定的径向和纬度坐标自由度的度量，使用库仑势与准Kinnersley横向框架。这些坐标是时空的不变量，可以用来明确地确定与准金纳斯利框架相关的突出的自旋-助推自由度（导致首选的准金纳斯利四分体（QKT））。在Kerr时空的小扰动极限下，这些坐标和QKT约化为Boyer-Lindquist坐标和Kinnersley四分体，而与模拟规范的选择无关。我们探索这种结构的性能分析和数值计算，我们获得的见解关于辐射的传播所描述的一个超级坡印廷矢量。我们还详细量化了所选四分体和量规的剥离性能。我们认为，这些选择是特别适合于一个快速收敛的波提取算法的提取位置接近无穷大，我们探讨数值上的程度，这一属性仍然适用于内部的计算域。使用一些额外的测试，我们验证了处方的行为，无论模拟量规在适当的限制要求。我们探讨的几何动机的坐标系的动态二元黑洞NR合并的行为，并发现他们有用的可视化功能NR模拟，如虚假的“垃圾”辐射。最后，我们仔细研究了两个黑洞的正面碰撞，例如，当它通过计算域移动时，提取的波形变化的方式。
英文摘要：
We investigate the suitability and properties of a quasi-Kinnersley tetrad and a geometrically motivated coordinate system as tools for quantifying both strong-field and wave-zone effects in numerical relativity (NR) simulations. We fix the radial and latitudinal coordinate degrees of freedom of the metric, using the Coulomb potential associated with the quasi-Kinnersley transverse frame. These coordinates are invariants of the spacetime and can be used to unambiguously fix the outstanding spin-boost freedom associated with the quasi-Kinnersley frame (resulting in a preferred quasi-Kinnersley tetrad (QKT)). In the limit of small perturbations about a Kerr spacetime, these coordinates and QKT reduce to Boyer-Lindquist coordinates and the Kinnersley tetrad, irrespective of the simulation gauge choice. We explore the properties of this construction both analytically and numerically, and we gain insights regarding the propagation of radiation described by a super-Poynting vector. We also quantify in detail the peeling properties of the chosen tetrad and gauge. We argue that these choices are particularly well suited for a rapidly converging wave-extraction algorithm as the extraction location approaches infinity, and we explore numerically the extent to which this property remains applicable on the interior of a computational domain. Using a number of additional tests, we verify that the prescription behaves as required in the appropriate limits regardless of simulation gauge. We explore the behavior of the geometrically motivated coordinate system in dynamical binary-black-hole NR mergers, and find them useful for visualizing features in NR simulations such as the spurious "junk" radiation. Finally, we carefully scrutinize the head-on collision of two black holes and, for example, the way in which the extracted waveform changes as it moves through the computational domain.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
