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. (Nat Phys 12:346, 2016), Barrera-Hinojosa and Li (GRAMSES: a new route to general relativistic N-body simulations in cosmology—I. Methodology and code description, 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 two-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.

中文翻译：

---

宇宙学N体模拟中相对论校正的检测

宇宙N体模拟是在大型并行计算机上完成的。这就需要使用简单的时间积分器，此外，还需要使用电势的网格近似。最近，Adamek等人。（Nat Phys 12：346，2016），Barrera-Hinojosa和Li（GRAMSES：通向广义相对论N的新途径宇宙学中的人体模拟 方法论和代码描述（2019年）已经开发了一般的相对论N体模拟，以捕获相对论效应，主要用于宇宙学目的。因此，我们问是否可以利用现有技术以数值方式检测出近日点进近等相对论效应。我们首先研究开普勒问题中的伪近日点偏移，这是所用积分方法的函数，然后是二维晶格上力的附加插值的函数。可以选择几种偏心距和半长轴。使用这些结果，我们可以预测哪些精度和晶格常数可以检测N体模拟中的相对论近日点推进。