宇宙学N体模拟中相对论修正的探测
The detection of relativistic corrections in cosmological N-body simulations
AI总结：
研究在宇宙学N体模拟中探测相对论修正的可行性，通过分析开普勒问题中的虚假近日点偏移，确定能探测相对论效应的参数窗口。
摘要：
宇宙学N体模拟在大规模并行计算机上进行。这使得必须使用简单的时间积分器，并且还要对势进行网格近似。最近，Adamek等人（2015）；Barrera-Hinojosa等人（2019）开发了广义相对论N体模拟，主要用于宇宙学目的以捕捉相对论效应。因此，我们询问，在现有技术下，像近日点进动这样的相对论效应是否能在数值上以相关精度被探测到。我们首先研究开普勒问题中作为所用积分方法函数的虚假近日点偏移，然后研究作为二维格子上力的附加插值函数的近日点偏移。这是针对几种偏心率和半长轴的选择进行的。利用这些结果，我们可以预测哪些精度和格点常数允许在N体模拟中探测到相对论近日点进动。我们发现，只有小的参数窗口——如偏心率、距中心物体的距离和史瓦西半径——才能在数值计算中探测到修正。
英文摘要：
Cosmological N-body simulations are done on massively parallel computers. This necessitates the use of simple time integrators, and, additionally, of mesh-grid approximations of the potentials. Recently, Adamek et al. (2015); Barrera-Hinojosa et al. (2019) have developed general relativistic N-body simulations to capture relativistic effects mainly for cosmological purposes. We therefore ask whether, with the available technology, relativistic effects like perihelion advance can be detected numerically to a relevant precision. We first study the spurious perihelion shift in the Kepler problem, as a function of the integration method used, and then as a function of an additional interpolation of forces on a 2-dimensional lattice. This is done for several choices of eccentricities and semi-major axes. Using these results, we can predict which precisions and lattice constants allow for a detection of the relativistic perihelion advance in N-body simulation. We find that there are only small windows of parameters -- such as eccentricity, distance from the central object and the Schwarzschild radius -- for which the corrections can be detected in the numerics.
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