关于平行于观测场的共形向量场
On Conformal Vector Fields Parallel to The Observer Field
摘要：
我们回顾了Hasse和Perlick的一个定理，该定理通过三个等价性质--即红移势的存在、平行于观测场的共形矢量场的存在、观测场剪切的消失以及一些可积性条件--建立了一个表征无引力宇宙模型的结果。我们能够提供一个简化的证明使用诺特定理计算守恒量沿类光测地线是与共形对称。由此我们得到了关于运动学不变量与红移各向同性的联系以及共形矢量场与时空因果关系的联系的更详细的信息。
英文摘要：
We review a theorem by Hasse and Perlick establishing a result characterizing parallax-free cosmological models via three equivalent properties -- namely the existence of a redshift potential, the existence of a conformal vector field parallel to the observer field, and the vanishing of the shear of the observer field together with some integrability condition. We are able to provide a simplified proof using Noether's theorem to calculate a conserved quantity along lightlike geodesics that is connected with the conformal symmetry. Thereby we derive more detailed information about the connection of the kinematical invariants to the redshift isotropy and the connection of conformal vector fields to the causality of spacetime.
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