Optical properties of a black hole - plasma system

In the first part of the thesis we summarize the formulation of relativistic geometric optics that includes optical effects of cold plasma with infinite conductivity, and its derivation through either Synge's approach or the high-frequency limit of Maxwell equations. In addition to the equations of motion for the photon, we also obtain the generalization of the geodesic deviation equation, which we termed 'ray deviation equation', and this allows us to investigate Etherington's theorem, generalized to the plasma case, as well as calculate the radiative flux. In the second part of the thesis, the theory is applied to the black hole - plasma system, the black hole described by Kerr geometry and the plasma described by one of several discussed toy models. We examine past-directed ray maps originating in the observation event, and we also study distribution of stars on the local sky of the observer positioned close to the black hole. Finally we suggest an algorithm that allows us to calculate a light curve from a continuous track of rays connecting the source and the observer. (author)