标题： 宇宙动力学：从欧拉框架到拉格朗日框架 - 一。牛顿近似 显示英文标题

标题： Cosmological dynamics: from the Eulerian to the Lagrangian frame - I. Newtonian approximation

摘要： 我们分析了在广义相对论的牛顿极限下，无压流体的非线性引力动力学，在欧拉和拉格朗日图像中都进行分析。 从泊松规范中的牛顿度规出发，我们转换到同步和共动规范，并在牛顿近似下得到拉格朗日度规。 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，则在任何阶数的微扰理论中都会准确地恢复所有项，只要它们是牛顿的。 我们明确展示了这一结果至二阶，并在两种规范中都进行了说明。 我们的变换澄清了在牛顿近似下从欧拉框架到拉格朗日框架的空间和时间坐标变化的意义。 显示英文摘要

摘要： 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.