Gravitational lensing in a non-uniform plasma
  We develop a model of gravitational lensing in a non-uniform plasma. When a
gravitating body is surrounded by a plasma, the lensing angle depends on the
frequency of the electromagnetic wave, due to dispersion properties of plasma,
in presence of a plasma inhomogeneity, and of a gravity. The second effect
leads, even in a uniform plasma, to a difference of the gravitational photon
deflection angle from the vacuum case, and to its dependence on the photon
frequency. We take into account both effects, and derive the expression for the
lensing angle in the case of a strongly nonuniform plasma in presence of the
gravitation. Dependence of the lensing angle on the photon frequency in a
homogeneous plasma resembles the properties of a refractive prism spectrometer,
which strongest action is for very long radiowaves. We discuss the
observational appearances of this effect for the gravitational lens with a
Schwarzschild metric, surrounded by a uniform plasma. We obtain formulae for
the lensing angle and the magnification factors in this case and discuss a
possibility of observation of this effect by the planned VLBI space project
Radioastron. We also consider models with a nonuniform plasma distribution. For
different gravitational lens models we compare the corrections to the vacuum
lensing due to the gravitational effect in plasma, and due to the plasma
inhomogeneity. We have shown that the gravitational effect could be detected in
the case of a hot gas in the gravitational field of a galaxy cluster.
