Inspiraling Black-Hole Binary Spacetimes: Transitioning from Analytical to Numerical Techniques
Inspiraling Black-Hole Binary Spacetimes: Transitioning from Analytical to Numerical Techniques
复制标题
鼓舞人心的黑洞二元时空：从分析技术过渡到数值技术
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
M. Zilhão
中科院分区：
文献类型：
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作者：
Y. Zlochower;H. Nakano;B. Mundim;M. Campanelli;S. Noble;M. Zilhão
在这里，我们探索如何使用数值模拟来扩展最近开发的分析黑洞双星时空，以包括合并本身。解析时空近似求解爱因斯坦场方程，双星分离得越远，近似误差就越小。重要的是，解析时空编码了辐射区中双星的过去历史以及扭曲每个黑洞的潮汐场。为了通过合并来延续时空，我们需要从解析时空平稳过渡到数值导出时空。为此，我们使用等质量、非旋转黑洞双星的解析时空作为度量后续数值演化的初始数据，并实验如何实现这种转变。我们测试了间隔 D=20M 的等质量双星的程序，并演化了六个轨道。我们发现，小的约束违规可能会产生大的动态影响，但可以通过使用约束阻尼系统（例如 Z4 系统的共形协变公式）来消除这些影响。我们发现随后的数值时空与后牛顿理论对后牛顿截断误差内的波形和吸气速率的预测之间存在一致性。
Here we explore how a recently developed analytical black-hole binary spacetime can be extended using numerical simulations to include the merger proper. The analytic spacetime solves the Einstein field equations approximately, with the approximation error becoming progressively smaller the more separated the binary. Importantly, the analytic spacetime encodes the past history of the binary in the radiation zone and the tidal fields distorting each black hole. To continue the spacetime through merger, we need to smoothly transition from the analytical spacetime to a numerically derived spacetime. We do this by using the analytical spacetime for an equal-mass, nonspinning black hole binary as initial data for a subsequent numerical evolution of the metric, and experiment with how this transition can be accomplished. We test our procedure for an equal-mass binary at a separation of D=20M, and evolve for six orbits. We find that small constraint violations can have large dynamical effects, but these can be removed by using a constraint damping system like the conformal covariant formulation of the Z4 system. We find agreement between the subsequent numerical spacetime and the predictions of post-Newtonian theory for the waveform and inspiral rate that is within the post-Newtonian truncation error.