Verification of Einstein’s Formula for Gravitational Deflection of Light Using Observations of Galactic Microlensing

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 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.