The Frequency-Shift in the Gravitational Microlensing
  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.
