Abstrakt
During his stay in Prague (April 1911-July 1912) Einstein concentrated on the construction of a new (relativistic) theory of gravity. Already in its first version he noticed that a light ray propagating close to the Sun will be bent by an amount which can be observed. He also indicated the possible existence of gravitational lenses. Since then the effects of bending and lensing have been studied in a great many both theoretical and observational papers confirming general relativity with a very high precision and limiting significantly various alternative theories of gravity. It was natural to assume that the sources of gravity (of bending) are surrounded by a vacuum; only recently the effects of surrounding media (typically plasma) have been considered.
In our contribution, we analyse both gravitational and plasma effects on the light rays propagating in several axisymmetric spacetimes of a physical interest. The deflection angles in vacuum and plasma medium are compared, it is shown how significantly they can differ. In particular, the Kerr and the Hartle-Thorne metrics are discussed, demonstrating the effects of different quadrupole moments of the gravitating source. An approximate analytical formula for the deflection angle in a weak gravitational field is derived for these spacetimes with plasma, and it is compared with some exact results. The inaccuracy arising from an approximate solution is discussed.
The light trajectories for several plasma profiles in these spacetimes are obtained and visualised explicitly. In addition, a general formula for the light deflection angle in an axially symmetric spacetime in plasma is given. And it is shown how this formula gets modified when it is applied for spherically symmetric spacetimes.