Abstract

General relativity (GR) has a solid experimental base. However, the emergence of new experimental capabilities and independent observational information stimulates continuing tests of general relativity. The purpose of this work is to evaluate the potential of gravitational microlensing of distant sources on the stars of our Galaxy and to verify Einstein’s formula of gravitational refraction. This effect has been repeatedly tested in the Solar System in high-accuracy experiments with the propagation of radio waves, when the measurements are most effective for the distances from the signal trajectory to the Sun on the order of several solar radii. In the case of galactic microlensing, a quite different type of observational data and other characteristic distances are used that are determined in the high magnification events by the Einstein ring radii, which is typically of the order of 1 AU. Although the gravitational deflections of light by stars are very small and currently practically inaccessible by direct measurements, nonetheless, due to the large distances to the microlenses, the radiation flux from the source in strong microlensing events can increase several times. To verify Einstein’s formula, a more general dependence of the beam deflection angle \(\alpha \propto 1/{{p}^{{1 + \varepsilon }}}\) on its impact distance p relative to the deflector is considered and, accordingly, the equations of gravitational lensing are modified. The challenge is to limit ε based on observational data. The Early Warning System data obtained in 2018 within the Optical Gravitational Lensing Experiment (OGLE) (http://ogle.astrouw.edu.pl/ogle4/ ews/2019/ews.html) was used. A sample of 100 light curves from the data obtained by the OGLE group in 2018 was formed. Each light curve was fitted as part of a modified model of gravitational lensing with parameter ε. As a result, 100 values of ε and estimates of their variances were obtained. It was found that the mean value of ε does not contradict GR within the limits of a one percent standard deviation. In the future, using a larger number of light curves will allow one to hope for a significant decrease in the error of ε due to statistical averaging.

中文翻译：

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使用银河微透镜观测值验证爱因斯坦公式的光引力偏转

摘要

广义相对论（GR）具有扎实的实验基础。但是，新的实验能力和独立的观测信息的出现刺激了对广义相对论的不断测试。这项工作的目的是评估银河系恒星上遥远源的引力微透镜的潜力，并验证爱因斯坦的引力折射公式。当测量对于从信号轨迹到太阳的距离（约为几个太阳半径）最有效时，这种影响已在太阳系中通过无线电波传播进行的高精度实验中反复测试。如果是银河微透镜，使用了完全不同类型的观测数据和其他特征距离，这些距离在高倍放大事件中由爱因斯坦环半径确定，通常为1 AU量级。尽管恒星的光的引力偏转非常小，并且目前几乎无法通过直接测量获得，但是由于与微透镜的距离较大，在强微透镜事件中来自光源的辐射通量可能会增加几倍。为了验证爱因斯坦公式，光束偏转角的更一般的依赖性 在强微透镜事件中，来自光源的辐射通量可能会增加几倍。为了验证爱因斯坦公式，光束偏转角的更一般的依赖性 在强微透镜事件中，来自光源的辐射通量可能会增加几倍。为了验证爱因斯坦公式，光束偏转角的更一般的依赖性\（\ alpha \ propto 1 / {{p} ^ {{1 + \ varepsilon}}} \）的影响距离p考虑到相对于偏转器的相对角，因此对引力透镜方程进行了修改。挑战在于根据观测数据限制ε。使用了2018年在光学引力透镜实验（OGLE）（http://ogle.astrouw.edu.pl/ogle4/ews/2019/ews.html）中获得的预警系统数据。从OGLE组在2018年获得的数据中形成了100条光曲线的样本。将每个光曲线拟合为参数ε的引力透镜修正模型的一部分。结果，获得了100个ε值及其方差的估计值。已经发现，在1％标准偏差的范围内，ε的平均值与GR没有矛盾。在将来，