数值双星演化过程中高效寻找黑洞自旋
Finding black hole spins efficiently during a numerical binary evolution
浏览论文内容
中文总结 AI 辅助
针对数值相对论代码SpEC中AKV自旋计算成本随分辨率升高而激增的问题，提出一种更快的AKV自旋计算新算法。
中文摘要 AI 辅助
双黑洞系统的动力学取决于其质量和自旋。对于有限间距的双星，无法以明确的方式定义这些量，但有几种合理的定义在无限间距极限下可归为预期值。近似基灵矢量（AKV）自旋是数值相对论代码SpEC中使用的自旋定义之一，AKV自旋需要在表观视界上寻找近似基灵矢量，这会归结为规模为$\boldsymbol{O}(L^2)$的广义特征值问题，直接求解的时间复杂度为$\boldsymbol{O}(L^6)$，其中$L$是表示表观视界所用的最高球谐模式。这种缩放意味着，随着我们以更高分辨率模拟系统，特别是高自旋或高质量比的系统，计算AKV自旋的成本会迅速增加。我们描述了一种新的AKV自旋计算算法，该算法比当前算法快得多。
英文摘要
The dynamics of a binary black hole system depend on its masses and spins. For a binary at finite separation, it is not possible to define these quantities in an unambiguous way; however, there are several reasonable definitions that reduce to the expected values in the limit of infinite separation. Approximate Killing vector (AKV) spin is one of the spin definitions used in the numerical relativity code SpEC. AKV spin requires finding approximate Killing vectors on an apparent horizon, which reduces to a generalized eigenvalue problem of size $\mathcal{O}(L^2)$, and a direct solve has time complexity $\mathcal{O}(L^6)$, where $L$ is the highest spherical harmonic mode used to represent the apparent horizon. This scaling means that the cost of computing AKV spins increases rapidly as we simulate systems at higher resolutions, especially those with high spin or mass ratios. We describe a new algorithm for computing AKV spins that is much faster than the current algorithm.
