New characterization of Robertson–Walker geometries involving a single timelike curve

IF 2 3区 物理与天体物理 Q2 PHYSICS, MATHEMATICAL
Marc Mars, Raül Vera
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引用次数: 0

Abstract

Our aim in this paper is two-fold. We establish a novel geometric characterization of the Robertson–Walker (RW) spacetime and, along the process, we find a canonical form of the RW metric associated to an arbitrary timelike curve and an arbitrary space frame. A known characterization establishes that a spacetime foliated by constant curvature leaves whose orthogonal flow (the cosmological flow) is geodesic, shear-free, and with constant expansion on each leaf, is RW. We generalize this characterization by relaxing the condition on the expansion. We show it suffices to demand that the spatial gradient and Laplacian of the cosmological expansion on a single arbitrary timelike curve vanish. In General Relativity these local conditions are equivalent to demanding that the energy flux measured by the cosmological flow, as well as its divergence, are zero on a single arbitrary timelike curve. The proof allows us to construct canonically adapted coordinates to the arbitrary curve, thus well-fitted to an observer with an arbitrary motion with respect to the cosmological flow.
涉及单条时间曲线的罗伯逊-沃克几何图形的新特征
本文的目的有两个方面。我们建立了罗伯逊-沃克(RW)时空的新几何特征,并在此过程中找到了与任意时间曲线和任意空间框架相关的 RW 度量的典型形式。一个已知的特征是,一个由恒定曲率叶片构成的时空,其正交流(宇宙学流)是测地的、无剪切的,并且在每个叶片上都有恒定的扩展,那么这个时空就是 RW 时空。我们通过放宽膨胀条件来概括这一特征。我们证明,只需要求宇宙膨胀在一条任意时间曲线上的空间梯度和拉普拉斯消失即可。在广义相对论中,这些局部条件等同于要求宇宙学流测量的能量通量及其发散在一条任意时间曲线上为零。通过证明,我们可以构建与任意曲线相适应的坐标,从而很好地适应相对于宇宙学流的任意运动的观测者。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
CiteScore
4.10
自引率
14.30%
发文量
542
审稿时长
1.9 months
期刊介绍: Publishing 50 issues a year, Journal of Physics A: Mathematical and Theoretical is a major journal of theoretical physics reporting research on the mathematical structures that describe fundamental processes of the physical world and on the analytical, computational and numerical methods for exploring these structures.
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