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 the dispersion properties of the plasma, in the presence of a plasma inhomogeneity, and of 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 non-uniform plasma in the presence of gravitation. The dependence of the lensing angle on the photon frequency in a homogeneous plasma resembles the properties of a refractive prism spectrometer, the strongest action of which is for very long radio waves. We discuss the observational appearance 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 the possibility of observation of this effect by the planned very long baseline interferometry space project RadioAstron. We also consider models with a non-uniform plasma distribution. For different gravitational lens models we compare the corrections to the vacuum lensing due to the gravitational effect in the plasma, and due to the plasma inhomogeneity. We show that the gravitational effect could be detected in the case of a hot gas in the gravitational field of a galaxy cluster.