arXiv 2007.159152020-07-31gr-qcmath-phmath.DGmath.MP

基于观测者的宇宙学模型不变量

Observer-based invariants for cosmological models

Lode Wylleman, Alan Coley, David McNutt, Matthew Aadne

备注：: 33 pages
发表信息：: 2019 Class. Quantum Grav. 36 235018

摘要：

考虑四维引力理论中宇宙学模型的等价性问题。一个宇宙学模型被认为是一个三元组$(M, {\bf g},{\bf u})$，由时空$(M, {\bf g})$和一个优选的归一化类时矢量场${\bf u}$组成，该矢量场与基本观测者的同余相切。我们介绍了一个修改的Cartan-Karlhede算法，通过限制适应于${\bf u}$的框架，包括协变导数的${\bf u}$以及黎曼张量及其协变导数。为了固定框架，我们利用相对于基本观察者的量，例如各向异性压力张量、能流矢量、Weyl张量的电和磁部分以及${\bf u}$的运动学量。这提供了一种更简单的方法来构造一个相对于基本观察者的不变量列表，该列表完全表征了模型，与坐标无关。作为算法的一个例子，我们考虑了几个著名的宇宙学模型从广义相对论。

英文摘要：

We consider the equivalence problem for cosmological models in four-dimensional gravity theories. A cosmological model is considered as a triple $(M, {\bf g},{\bf u})$ consisting of a spacetime $(M, {\bf g})$ and a preferred normalized time-like vector field ${\bf u}$ tangent to a congruence of fundamental observers. We introduce a modification of the Cartan-Karlhede algorithm by restricting to frames adapted to ${\bf u}$ and including the covariant derivatives of ${\bf u}$ along with the Riemann tensor and its covariant derivatives. To fix the frame we make use of quantities relative to the fundamental observers, such as the anisotropic pressure tensor, energy flux vector, electric and magnetic parts of the Weyl tensor and the kinematical quantities of ${\bf u}$. This provides a simpler way to construct a list of invariants relative to the fundamental observers that completely characterizes the model, independent of coordinates. As an illustration of the algorithm, we consider several well-known cosmological models from General Relativity.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

相关论文