论文标题
Szekeres几何形状的旋转，嵌入和拓扑
Rotation, Embedding and Topology for the Szekeres Geometry
论文作者
论文摘要
关于Szekeres不均匀宇宙学模型的最新工作发现了令人惊讶的旋转效果。 Hellaby表明，Angular $（θ，ϕ）$坐标没有恒定方向，而Buckley和Schlegel为从外壳到外壳的旋转速率以及3个空间嵌入平坦的4-D Euclidean空间时提供了明确的表达式。在这里，我们研究了该嵌入的某些属性，对于准球形的回忆案例，并使用它来证明两组结果完全一致。我们还展示了如何构建沿“径向”方向封闭的Szekeres模型，因此具有“自然”的嵌入式圆环拓扑结构。几种明确的模型说明了嵌入以及壳旋转和倾斜效果。
Recent work on the Szekeres inhomogeneous cosmological models uncovered a surprising rotation effect. Hellaby showed that the angular $(θ, ϕ)$ coordinates do not have a constant orientation, while Buckley and Schlegel provided explicit expressions for the rate of rotation from shell to shell, as well as the rate of tilt when the 3-space is embedded in a flat 4-d Euclidean space. We here investigate some properties of this embedding, for the quasi-spherical recollapsing case, and use it to show that the two sets of results are in complete agreement. We also show how to construct Szekeres models that are closed in the 'radial' direction, and hence have a 'natural' embedded torus topology. Several explicit models illustrate the embedding as well as the shell rotation and tilt effects.
