Frame dragging and Eulerian frames in General Relativity
Frame dragging and Eulerian frames in General Relativity
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广义相对论中的框架拖动和欧拉框架
DOI：
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发表时间：
2013
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通讯作者：
Cornelius Rampf
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作者：
Cornelius Rampf
通过将Bertschinger泊松规范与欧拉参照系联系起来，阐明了冷暗物质扰动的物理解释。我们通过使用拉格朗日方法来形成相对论宇宙结构来获得这样的关联。显式地，我们从爱因斯坦方程在同步/共转坐标系中的二阶解开始，它定义了拉格朗日标架，并将其变换到泊松坐标系。这种坐标/规范变换的生成矢量是相对论位移场。泊松坐标系中的度规微扰包含标准/欧拉牛顿微扰理论的已知结果，但也包含纯粹的相对论修正。在次视界尺度上，这些相对论修正主要由牛顿主体部分主导。然而，这些校正为密度和速度设置了非线性(初始)约束，这些约束在接近地平线的比例上变得重要。此外，我们报道了位移场中横向分量的出现，并发现它引起了像欧拉标架中所看到的非线性标架拖曳，这种拖曳在后期和次水平尺度上是次要的。最后，我们找到了另外两个可以与欧拉标架相关联的标尺。我们认为泊松规更可取，因为它有最简单的物理解释。
The physical interpretation of cold dark matter perturbations is clarified by associating Bertschinger’s Poisson gauge with a Eulerian frame of reference. We obtain such an association by using a Lagrangian approach to relativistic cosmological structure formation. Explicitly, we begin with the second-order solution of the Einstein equations in a synchronous/comoving coordinate system, which defines the Lagrangian frame, and transform it to a Poissonian coordinate system. The generating vector of this coordinate/gauge transformation is found to be the relativistic displacement field. The metric perturbations in the Poissonian coordinate system contain known results from standard/Eulerian Newtonian perturbation theory, but contain also purely relativistic corrections. On subhorizon scales, these relativistic corrections are dominated by the Newtonian bulk part. These corrections, however, set up nonlinear (initial) constraints for the density and for the velocity that become important on scales close to the horizon. Furthermore, we report the occurrence of a transverse component in the displacement field, and find that it induces a nonlinear frame dragging as seen in the Eulerian frame, which is subdominant at late times and subhorizon scales. Finally, we find two other gauges that can be associated with a Eulerian frame. We argue that the Poisson gauge is to be preferred because it comes with the simplest physical interpretation.