arXiv 1807.063532018-07-17gr-qcmath-phmath.MP

广义相对论的一般模型

The generic model of General Relativity

Michael Tsamparlis, Andronikos Paliathanasis

备注：: 55 pages, no figures
发表信息：: Arab. J. Math. 8, 201 (2019)
DOI：: 10.1007/s40065-019-0239-7

摘要：

我们在广义相对论中建立了一个通用的时空模型，它可以用来建立广义相对论中的任何引力模型。一般模型使用两种类型的假设：（a）几何假设额外的时空黎曼几何的固有几何恒等式和（b）假设定义一类观察者的4-速度$u^{a}$，这是一个单位类时向量场。几何假设通常涉及对称性假设（所谓的直射）。后者介绍了时空中张量场的1 + 3分解。1 + 3分解导致两个主要结果。$u_{a;b}$的1 + 3分解定义了模型的运动学变量（膨胀、旋转、剪切和4-加速度），并定义了重力模型的运动学。代表所有引力物质的能量动量张量的1 + 3分解引入了由定义的观测者测量的模型的动态变量（能量密度、各向同性压力、动量传递或热通量矢量和各向异性压力的无痕张量），并定义了模型的动态。由模型假设的对称性作为对模型的运动学和动力学变量的约束。作为一般模型的第二个进一步发展，我们假设除了观测者的4-速度$u_{a}$之外，时空中还存在第二个普适向量场$n_{a}$，从而具有所谓的双同余$(u_{a},n_{a})$，它可以用来定义张量场的1 + 1 + 2分解。1 + 1 + 2分解导致一个扩展的运动学关于两个领域建设的双同余和一个更精细的动力学涉及更多的物理变量。

英文摘要：

We develop a generic spacetime model in General Relativity which can be used to build any gravitational model within General Relativity. The generic model uses two types of assumptions: (a) Geometric assumptions additional to the inherent geometric identities of the Riemannian geometry of spacetime and (b) Assumptions defining a class of observers by means of their 4-velocity $u^{a}$ which is a unit timelike vector field. The geometric assumptions as a rule concern symmetry assumptions (the so called collineations). The latter introduces the 1+3 decomposition of tensor fields in spacetime. The 1+3 decomposition results in two major results. The 1+3 decomposition of $u_{a;b}$ defines the kinematic variables of the model (expansion, rotation, shear and 4-acceleration) and defines the kinematics of the gravitational model. The 1+3 decomposition of the energy momentum tensor representing all gravitating matter introduces the dynamic variables of the model (energy density, the isotropic pressure, the momentum transfer or heat flux vector and the traceless tensor of the anisotropic pressure) as measured by the defined observers and define the dynamics of he model. The symmetries assumed by the model act as constraints on both the kinematical and the dynamical variables of the model. As a second further development of the generic model we assume that in addition to the 4-velocity of the observers $u_{a}$ there exists a second universal vector field $n_{a}$ in spacetime so that one has a so called double congruence $(u_{a},n_{a})$ which can be used to define the 1+1+2 decomposition of tensor fields. The 1+1+2 decomposition leads to an extended kinematics concerning both fields building the double congruence and to a finer dynamics involving more physical variables.

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：

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