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arXiv 1703.01367gr-qchep-th
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de Sitter和反de Sitter时空的又一对角度量族

Yet another family of diagonal metrics for de Sitter and anti-de Sitter spacetimes

Jiri Podolsky, Ondrej Hruska

摘要:

在这项工作中,我们提出并分析了一类新的坐标表示德西特和反德西特时空的度量是对角和(通常)静态和轴对称的。与这些基本几何的众所周知的形式相反,这些基本几何通常对应于具有恒定空间曲率的3-空间的1+3叶理,新的度量适合于2+2叶理,并且是两个2-常曲率空间的翘曲产物。这类新的(反)de Sitter度规依赖于宇宙学常数λ和与2-空间曲率有关的两个离散参数+1,0,-1.这个类对于Lambda>0有3个不同的子情形,对于Lambda<0有8个子情形。我们系统地研究了所有这些可能性。特别是,我们明确提出了相应的参数化的(反)德西特双曲面,可视化的坐标线和曲面内的全球共形圆柱,调查他们的相互关系,提出了一些密切相关的形式的度量,并给出转换标准德西特和反德西特度量。利用这些结果,我们还提供了一个物理解释的B-度规作为精确的引力场的快子。

英文摘要:

In this work we present and analyze a new class of coordinate representations of de Sitter and anti-de Sitter spacetimes for which the metrics are diagonal and (typically) static and axially symmetric. Contrary to the well-known forms of these fundamental geometries, that usually correspond to a 1+3 foliation with the 3-space of a constant spatial curvature, the new metrics are adapted to a 2+2 foliation, and are warped products of two 2-spaces of constant curvature. This new class of (anti-)de Sitter metrics depends on the value of cosmological constant Lambda and two discrete parameters +1,0,-1 related to the curvature of the 2-spaces. The class admits 3 distinct subcases for Lambda>0 and 8 subcases for Lambda<0. We systematically study all these possibilities. In particular, we explicitly present the corresponding parametrizations of the (anti-)de Sitter hyperboloid, visualize the coordinate lines and surfaces within the global conformal cylinder, investigate their mutual relations, present some closely related forms of the metrics, and give transformations to standard de Sitter and anti-de Sitter metrics. Using these results, we also provide a physical interpretation of B-metrics as exact gravitational fields of a tachyon.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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