PROFESSOR AHMEDOV B.J.

The shadow of a rotating (i) non-Kerr, (ii) Horava-Lifshitz, (iii) Kerr-Taub-NUT, (iv) five-dimensional rotating Myers-Perry and other black holes in vacuum has been studied, and it has been shown that in addition to the specific angular momentum, (i) the deformation parameter of non-Kerr spacetime, (ii) parameters of Horava-Lifshitz spacetime, (iii) nonvanishing gravitomagnetic charge, and other parameters essentially deform the shape of the black hole shadow. A comparison of the obtained theoretical results on the polarization angle with the observational data on Faraday rotation measurements provides the upper limit for the dimensionless deformation parameter as e<19, the upper limit for the Horava-Lifshitz d parameter as d = 2.1•10-3 etc. Then gravitational lensing in the vicinity of a slowly rotating massive object surrounded by plasma has been studied. The obtained deflection angle of the light ray in the presence of plasma depends on (i) the frequency of the electromagnetic wave, due to the dispersion properties of the plasma; (ii) the gravitational mass M; and (iii) the angular momentum of the gravitational lens. We have studied photon motion around axially symmetric rotating (i) Kerr black hole, (ii) wormhole in the presence of a plasma with radial power-law density. It is shown that in the presence of a plasma, the observed shape and size of the shadow of rotating (i) Kerr black hole, (ii) wormhole changes depending on the (i) plasma parameters, (ii) gravitational object spin, and (iii) inclination angle between the observer plane and the axis of rotation of the black hole/wormhole. Finally, we have developed a general formalism to describe the black hole shadow as an arbitrary polar curve expressed in terms of a Legendre expansion. New developed formalism does not presume any knowledge of the properties of the shadow, e.g., the location of its center, and offers a number of routes to characterize the distortions of the curve with respect to reference circles. These distortions can be implemented in a coordinate independent manner by different teams analyzing the same data. It has been shown that the new formalism provides an accurate and robust description of noisy observational data, with smaller error variances when compared to previous measurements of the distortion.