时空各向异性：理论问题和观测检验的可能性
Space-time anisotropy: theoretical issues and the possibility of an observational test
摘要：
在过去十年中收集的具体天体物理数据导致需要修改Einstein-Hilbert作用量的表达式，并且已知有几种尝试可以满足这一需要。本文提出的修正源于时空可能的各向异性，即最小作用量原理中最简单标量的自然变化。为了给这一观点提供可检验的支持，我们提出了光学测量参量共振--一种基于宇宙微波激射器电磁辐射与近距离双系统或脉冲星发射的周期性引力波相互作用的银河系尺度实验。由于这种效应取决于时空度规，因此可能的各向异性可以通过观测来揭示。为了给出相应的理论来预测对实验预期结果的修正，选择了芬斯勒几何的特定数学形式。结果表明，在时空各向异性存在的情况下，适合观测的天体物理系统的方向会显示出各向异性，在所得到的测地线方程中存在一个方向依赖项。
英文摘要：
The specific astrophysical data collected during the last decade causes the need for the modification of the expression for the Einstein-Hilbert action, and several attempts sufficing this need are known. The modification suggested in this paper stems from the possible anisotropy of space-time and this means the natural change of the simplest scalar in the least action principle. To provide the testable support to this idea, the optic-metrical parametric resonance is regarded - an experiment on the galactic scale based on the interaction between the electromagnetic radiation of cosmic masers and periodical gravitational waves emitted by close double systems or pulsars. Since the effect depends on the space-time metric, the possible anisotropy could reveal itself through observations. To give the corresponding theory predicting the corrections to the expected results of the experiment, the specific mathematical formalism of Finsler geometry was chosen. It was found that in case the anisotropy of the space-time exists, the orientation of the astrophysical systems suitable for observations would show it. In the obtained geodesics equation there is a direction dependent term.
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