标题： 无剪切、无旋、测地线、各向异性流体宇宙学 显示英文标题

标题： Shear-free, Irrotational, Geodesic, Anisotropic Fluid Cosmologies

摘要： 研究了流体流动线形成无剪切、无旋转、测地类时共轭的广义相对论各向异性流体模型。 这些模型属于Petrov类型D，并假设热通量为零，且各向异性应力张量具有两个不同的非零本征值。 建立了一些关于这些模型的度规和应力张量形式的一般结果。 此外，如果由共动观测者测量的能量密度和各向同性压强满足形式为$p = p(\mu)$的状态方程，其中$\frac{dp}{d\mu} \neq -\frac{1}{3}$，那么这些时空允许由常数Ricci标量的空间类超曲面组成的叶状结构。 此外，还研究了能量密度和各向异性压强仅依赖于时间的模型；发现了空间齐次和空间非齐次模型。 对这些模型进行了分类。 此外，还研究了一类各向异性流体模型，这些模型是均匀各向同性宇宙模型的简单推广。 显示英文摘要

摘要： General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress-tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a comoving observer, satisfy an equation of state of the form $p = p(\mu)$, with $\frac{dp}{d\mu} \neq -\frac{1}{3}$, then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.