In this work we suggest that higher-dimensional modifications to the matter content in FRW spacetimes can be obtained not only, as first considered by Ponce de Leon, referring to "moving" 4D hypersurfaces non-orthogonal to the time-dependent extra dimension of an embedding 5D manifold, but also referring to "fixed" 4D hypersurfaces orthogonal to a suitable scalar function which defines a static foliation of the 5D manifold and takes the role of the extra dimension in a suitable coordinate system. Results obtained in each approach crucially depend on the method used to identify the 4D metric of our brane universe from the 5D metric of the bulk manifold.
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机译：在这项工作中，我们建议，不仅像庞塞·德·利昂（Ponce de Leon）首先考虑的那样，是指对FRW时空中的物质含量进行高维修改，这是指将“ 4D”超曲面“正交于”随时间变化的额外维数。嵌入5D流形，但也指与合适的标量函数正交的“固定” 4D超曲面，标量函数定义5D流形的静态叶面并在合适的坐标系中承担额外尺寸的作用。每种方法获得的结果都至关重要地取决于用于从大体积歧管的5D度量标准中识别我们的麸皮宇宙的4D度量标准的方法。
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