Gravitational Lensing in Plasmic Medium
  The influence of plasma on different effects of gravitational lensing is
reviewed. Using the Hamiltonian approach for geometrical optics in a medium in
the presence of gravity, an exact formula for the photon deflection angle by a
black hole (or another body with a Schwarzschild metric) embedded in plasma
with a spherically symmetric density distribution is derived. The deflection
angle in this case is determined by the mutual combination of different
factors: gravity, dispersion, and refraction. While the effects of deflection
by the gravity in vacuum and the refractive deflection in a nonhomogeneous
medium are well known, the new effect is that, in the case of a homogeneous
plasma, in the absence of refractive deflection, the gravitational deflection
differs from the vacuum deflection and depends on the photon frequency. In the
presence of a plasma nonhomogeneity, the chromatic refractive deflection also
occurs, so the presence of plasma always makes gravitational lensing chromatic.
In particular, the presence of plasma leads to different angular positions of
the same image if it is observed at different wavelengths. It is discussed in
detail how to apply the presented formulas for the calculation of the
deflection angle in different situations. Gravitational lensing in plasma
beyond the weak deflection approximation is also considered.
