  We show that observation of the time-dependent effect of microlensing of
relativistically broadened emission lines (such as e.g. the Fe Kalpha line in
X-rays) in strongly lensed quasars could provide data on celestial mechanics of
circular orbits in the direct vicinity of the horizon of supermassive black
holes. This information can be extracted from the observation of evolution of
red / blue edge of the magnified line just before and just after the period of
crossing of the innermost stable circular orbit by the microlensing caustic.
The functional form of this evolution is insensitive to numerous astrophysical
parameters of the accreting black hole and of the microlensing caustics network
system (as opposed to the evolution the full line spectrum). Measurement of the
temporal evolution of the red / blue edge could provide a precision measurement
of the radial dependence of the gravitational redshift and of velocity of the
circular orbits, down to the innermost stable circular orbit. These
measurements could be used to discriminate between the General Relativity and
alternative models of the relativistic gravity in which the dynamics of photons
and massive bodies orbiting the gravitating centre is different from that of
the geodesics in the Schwarzschild or Kerr space-times.
