Gravitational lensing in a non-uniform plasma

Abstract

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.Comment: 12 pages, 3 figure

Gravitational lensing in plasma: Relativistic images at homogeneous plasma

“…In [27,28] we have found that in the absence of refraction, in a uniform dispersive medium, when the refractive index depends on the photon frequency, the gravitational deflection is qualitatively different from the vacuum case, and the deflection angle depends on the photon frequency (see Fig. 3).…”

“…Applying the general theory to plasma, that is a dispersive medium, and its refractive index depends on the photon frequency, we have obtained a simple analytical formula for the light deflection in a Schwarzschild metric, in presence of a homogeneous plasma [27]. In [28] we developed a more general approach, considering an inhomogeneous plasma, where a nongravitating refractive deflection was also taken into account. All the results have been obtained in the approximation of a small deflection angle.…”

“…The consideration of the photon deflection by a gravitating center, in presence of plasma around it, was considered in a classical book of problems [26]; for more details see our previous works [27,28]. In application to gravitational lensing it was discussed in [29] where gravitational lensing by the gravitating body with surrounding spherically symmetric plasma distribution was considered.…”

Optical properties of black holes in the presence of a plasma: The shadow

“…Now using the Hamilton-Jacobi equation which defines the equation of motion of the photons for a given space-time geometry [4,22,24]:…”

“…For example, the gravitational lensing in inhomogeneous and homogeneous plasma around black holes has been recently studied in [4][5][6][7][8] as extension of vacuum studies (see, e.g. [9,10]).…”