Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation
Cosmological dynamics: from the Eulerian to the Lagrangian frame. Part I. Newtonian approximation
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宇宙动力学：从欧拉框架到拉格朗日框架。
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
D. Maino
中科院分区：
文献类型：
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作者：
E. Villa;S. Matarrese;D. Maino
在欧拉图和拉格朗日图中，我们分析了广义相对论牛顿极限中无压流体的非线性引力动力学。从泊松规范中的牛顿度规出发，将其转化为同步规范和旋转规范，得到了牛顿近似下的拉格朗日度规。我们的方法是完全非微扰的，这意味着如果我们的量按照标准微扰理论的规则展开，那么微扰理论中的所有项都可以精确地恢复到任何阶数，只要它们是牛顿的。我们显式地给出了这一结果，直到二阶和两种量规。我们的变换阐明了在牛顿近似下，空间和时间坐标从欧拉坐标到拉格朗日坐标的变化的意义。
We analyse the non-linear gravitational dynamics of a pressure-less fluid in the Newtonian limit of General Relativity in both the Eulerian and Lagrangian pictures. Starting from the Newtonian metric in the Poisson gauge, we transform to the synchronous and comoving gauge and obtain the Lagrangian metric within the Newtonian approximation. Our approach is fully non-perturbative, which implies that if our quantities are expanded according to the rules of standard perturbation theory, all terms are exactly recovered at any order in perturbation theory, only provided they are Newtonian. We explicitly show this result up to second order and in both gauges. Our transformation clarifies the meaning of the change of spatial and time coordinates from the Eulerian to the Lagrangian frame in the Newtonian approximation.