# The Frequency-Shift in the Gravitational Microlensing

## TL;DR

This paper proposes using the relativistic frequency shift caused by the relative transverse velocity in gravitational microlensing to measure lens parameters, utilizing high-precision spectrographs and combining data from space-based parallax and proper motion measurements.

## Contribution

It introduces a novel method to determine lens mass and velocity in microlensing by detecting frequency shifts with advanced spectrographs, integrating multiple observational techniques.

## Key findings

- Potential to measure lens masses from black holes to planets.
- Feasibility of detecting frequency shifts with $10^{-11}$ accuracy.
- Combines spectroscopic, parallax, and proper motion data for comprehensive analysis.

## Abstract

The relative transverse velocity of a lens with respect to the source star in gravitational lensing results in a frequency shift in the light rays passing by a lens. We propose using this relativistic effect for measuring the relative velocity of the lens with respect to the source star in gravitational microlensing. High precision spectrographs with the accuracy of detecting the relative frequency shift in the order of $10^{-11}$ will enable us to measure this effect in the microlensing events. The spectrographs such as ESPRESSO is going to be used for detecting exoplanets with the accuracy of the radial velocity of $0.1$~m/s. This kind of instrument can be used in follow-up observations of the microlensing events. Combining the spectroscopic observation with the parallax measurements of microlensing events from space and proper motion of the source stars with GAIA telescope enables us to measure all the parameters of the microlensing events. The result would be measuring the mass and the transverse velocity of lenses with the masses in the range of the black holes to the free-floating planets.