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首页> 外文期刊>Bulletin of the American Physical Society >APS -Annual Meeting of the APS Four Corners Section- Event - Symmetries of Geodesics for Homogeneous Gravitational Fields
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APS -Annual Meeting of the APS Four Corners Section- Event - Symmetries of Geodesics for Homogeneous Gravitational Fields

机译：APS-APS四角分会年会-活动-均匀重力场的测地线对称性

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In Einstein's general theory of relativity freely falling test particles follow geodesics of the spacetime geometry. Some geodesics have symmetries, known as affine collineations. Mathematically, these affine collineations are transformations that preserve the connection defined by the metric, without preserving the metric. Physically, they change the notion of lengths and angles, while preserving the notion of parallelism. Associated with each affine collineation are two conserved quantities. Previously these quantities were understood to be non-Noetherian, however we show that they can be derived from a direct application of Noether's theorem. We calculate all affine collineations and their corresponding conservation laws for all of the homogeneous solutions to the Einstein Field Equations in vacuum, with perfect fluid sources, and with homogeneous electromagnetic sources.
机译：在爱因斯坦的广义相对论中，自由落下的测试粒子遵循时空几何的测地线。一些测地线具有对称性，称为仿射归类。从数学上讲，这些仿射归类是保留度量标准定义的连接但不保留度量标准的转换。从物理上讲，它们会更改长度和角度的概念，同时保留并行性的概念。与每个仿射归类相关联的是两个保守量。以前，这些量被理解为非Noether量，但是我们证明了它们可以从Noether定理的直接应用中得出。我们在真空，理想流体源和均匀电磁源的情况下，计算出爱因斯坦场方程的所有齐次解的所有仿射归类及其相应的守恒律。

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