标题： 相对论宇宙学中几何场的因果传播 显示英文标题

标题： Causal propagation of geometrical fields in relativistic cosmology

摘要： 我们采用扩展的1+3正交框架形式化方法，用于流体时空几何$({\cal M}, {\bf g}, {\bf u})$，该方法包含Weyl曲率的Bianchi场方程，以推导一组几何定义的动力场变量的一阶对称双曲形式的44-D演化系统。 通过用一种流体动力学的完美流体来描述物质源场，相对于随物质运动的观察者（其空间参考系由Fermi传播）的扰动传播速度$v$，在物质和引力场中的扰动，由系统的特征3-面表示为波前，得到。 特别是，发现Weyl曲率导致两个（非洛伦兹不变的）类似库仑的特征本征场以$v = 0$传播，以及四个横向特征本征场以$|v| = 1$传播，这些是众所周知的，还有四个（非洛伦兹不变的）纵向特征本征场以$|v| = \sfrac{1}{2}$传播。 详细讨论了这一结果的含义，并与物质分布中不规则性的传播进行了类比。 在一个实例中，我们将方程特化为局部旋转对称II类宇宙模型，并将约束条件纳入因果传播的动力变量集合中。 显示英文摘要

摘要： We employ the extended 1+3 orthonormal frame formalism for fluid spacetime geometries $({\cal M}, {\bf g}, {\bf u})$, which contains the Bianchi field equations for the Weyl curvature, to derive a 44-D evolution system of first-order symmetric hyperbolic form for a set of geometrically defined dynamical field variables. Describing the matter source fields phenomenologically in terms of a barotropic perfect fluid, the propagation velocities $v$ (with respect to matter-comoving observers that Fermi-propagate their spatial reference frames) of disturbances in the matter and the gravitational field, represented as wavefronts by the characteristic 3-surfaces of the system, are obtained. In particular, the Weyl curvature is found to account for two (non-Lorentz-invariant) Coulomb-like characteristic eigenfields propagating with $v = 0$ and four transverse characteristic eigenfields propagating with $|v| = 1$, which are well known, and four (non-Lorentz-invariant) longitudinal characteristic eigenfields propagating with $|v| = \sfrac{1}{2}$. The implications of this result are discussed in some detail and a parallel is drawn to the propagation of irregularities in the matter distribution. In a worked example, we specialise the equations to cosmological models in locally rotationally symmetric class II and include the constraints into the set of causally propagating dynamical variables.