General relativistic N-body simulations in the weak field limit
General relativistic N-body simulations in the weak field limit
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DOI：
10.1103/physrevd.88.103527
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发表时间：
2013-11-22
影响因子：
5
通讯作者：
Kunz, Martin
中科院分区：
文献类型：
--
作者：
Adamek, Julian;Daverio, David;Kunz, Martin
我们开发了一种适合于宇宙学应用的弱场下广义相对论n体模拟的形式。通过保留一阶的度规扰动，一阶的二阶导数和所有阶的二阶导数，从而考虑到爱因斯坦引力最重要的非线性效应，使问题保持易于处理。预计任何重大的“反向反应”都应按此顺序出现。我们通过在平面对称情况下实现该模拟方案并运行两个测试用例（一个只包含冷暗物质，另一个也包含宇宙常数）来证明该模拟方案在实践中是可行的。对于这些平面对称的情况，与通常的牛顿n体模拟的偏差仍然很小，除了对背景进行非平凡的修正外，可以在牛顿框架内准确估计。对背景尺度因子的修正是一种真正的反作用力，该算法可以鲁棒地得到。我们的数值方法也自然地适合于包含额外的相对论场，因此适合于暗能量或修正的重力模拟。
We develop a formalism for general relativistic N-body simulations in the weak field regime, suitable for cosmological applications. The problem is kept tractable by retaining the metric perturbations to first order, the first derivatives to second order, and second derivatives to all orders, thus taking into account the most important nonlinear effects of Einstein gravity. It is also expected that any significant "backreaction" should appear at this order. We show that the simulation scheme is feasible in practice by implementing it for a plane-symmetric situation and running two test cases, one with only cold dark matter, and one which also includes a cosmological constant. For these plane-symmetric situations, the deviations from the usual Newtonian N-body simulations remain small and, apart from a nontrivial correction to the background, can be accurately estimated within the Newtonian framework. The correction to the background scale factor, which is a genuine backreaction effect, can be robustly obtained with our algorithm. Our numerical approach is also naturally suited for the inclusion of extra relativistic fields and thus for dark energy or modified gravity simulations.