K‐surfaces in the Schwarzschild space‐time and the construction of lattice cosmologies
K‐surfaces in the Schwarzschild space‐time and the construction of lattice cosmologies
复制标题
史瓦西时空中的K面和晶格宇宙论的构建
DOI：
--
复制
发表时间：
1980
期刊：
影响因子：
--
通讯作者：
J. Isenberg
中科院分区：
文献类型：
--
作者：
D. Brill;J. Cavallo;J. Isenberg
研究了球对称静态时空中具有恒定平均曲率K的类空间球对称超曲面（我们称之为K‐曲面）。我们利用变分原理得到了这些曲面所满足的微分方程。时空杀伤矢量导致以有效势运动的粒子的能量守恒形式的第一个积分。K曲面在平面空间内的固有几何嵌入同样源于有效势运动。我们将形式主义应用于Schwarzschild解，并展示了各种K‐曲面及其平坦空间嵌入的数值积分结果。我们利用这些构造了“晶格”宇宙学模型，并获得了具有开放和封闭弗里德曼型大尺度行为的K‐曲面的叶理。
We investigate spacelike spherically symmetric hypersurfaces of constant mean curvature K (which we call K‐surfaces) in spherically symmetric static spacetimes. We obtain the differential equation satisfied by these surfaces from a variational principle. The spacetime Killing vector leads to a first integral in the form of a conservation of energy for a particle moving in an effective potential. An embedding of the K‐surfaces’ intrinsic geometry in flat space likewise follows from an effective potential motion. We apply the formalism to the Schwarzschild solution, and display results of numerical integrations for a variety of K‐surfaces and their flat space embeddings. We use these to construct ’’lattice’’ cosmological models, and obtain a foliation of K‐surfaces of such models with large scale behavior of both the open and closed Friedmann type.