离散时空中的奇性自由的Friedmann宇宙解

由尘埃物质粒子的集合来形成一个理想的离散时空的Friedmann宇宙模型并证明了它是奇性 自由的. 关键词： 离散时空 尘埃物质 Friedmann宇宙 奇性自由     

离散时空中的非塌缩的尘埃球解

引进了实数的层次性与离散化，将连续函数理论加以改进和推广为离散函数理论，并基于由离散函数理论所表示的经典广义相对论来讨论尘埃物质的引力塌缩问题，指出了关于这个问题的连续体系的Oppenheimer 和Snyder解中的Friedmann内解与Schwarzschild外解的不完整性并加以拓展和离散化，导出了一种非塌缩的尘埃物质结构，消除了引力奇性并揭示了时空离散化的深刻性质. 关键词： 离散实数 离散时空 广义相对论 Oppenheimer 和Snyder解 奇性自由     

A singularity theorem based on spatial averages

Inspired by Raychaudhuri’s work, and using the equation named after him as a basic ingredient, a new singularity theorem is proved. Open non-rotating Universes, expanding everywhere with a non-vanishing spatial average of the matter variables, show severe geodesic incompletness in the past. Another way of stating the result is that, under the same conditions, any singularity-free model must have a vanishing spatial average of the energy density (and other physical variables). This is very satisfactory and provides a clear decisive difference between singular and non-singular cosmologies. In memory of Amal Kumar Raychaudhuri (1924–2005).     

On singularity-free spacetimes

We consider here the metric for the singularity-free family of fluid models. The metric is unique for cylindrically symmetric space-time with metric potentials being separable functions of radial and time coordinates in the comoving coordinates. It turns out that fluid models separate out into two classes, withρ ≠μp in general butρ = 3p in particular andp =ρ. It is shown that in both the cases radial heat flow can be incorporated without disturbing the singularity-free character of the spacetime. The geodesics of the singularity-free metric are studied and the geodesic completeness is established. Several previously known solutions are derived as particular cases.