Propagation of light signals near a black hole surrounded by a plasma

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Whereas 30 years ago black holes were just hypothetical objects allowed by Einstein's theory of general relativity, we have now strong observational evidence that they actually exist in Nature. The information we can get about a black hole comes mainly from its effects on light signals (including signals beyond the optical spectrum) that come close to the black hole. In this project we are planning to investigate two such effects, considering light propagation not only in vacuo but also in a plasma which is of relevance for radio signals. (a) Firstly we want to calculate the travel times of signals from a pulsar that orbits a black hole. In contrast to earlier studies of this problem we want to take the effects of an inhomogeneous plasma into account that surrounds the black hole. (b) Secondly we want to consider light from a (small but extended) source that orbits a black hole and emits isotropically in its rest frame. The light source may be interpreted as a hot spot in an accretion disc. In particular, we want to consider the case that the light source is spinning about its axis and the influence of the spin on the emitted radiation is to be taken into account. After doing this for light propagation in a vacuum, we also want to take the effects of an inhomogeneous plasma into account. This has interesting applications, even for the case that the source is non-spinning: Modelling a radiating rotating disc around a black hole as consisting of many orbiting light sources allows to calculate the influence of a plasma on the visual appearance of such a disc. In all cases, it is our goal to derive exact analytical formulas as far as possible and to use analytical apporoximation methods otherwise. The black hole is mainly to be modelled by the Schwarzschild or the Kerr spacetime, but other metrics (black holes of alternative theories and black hole impostors like wormholes) will be partly included in the investigation as well. A main motivation for this project comes from already existing or expectable observations of (supermassive or stellar) black holes. Analytic formulas for the influence of a plasma on the radiation emitted by orbiting light sources would be important tools for evaluating these observations and interpreting them correctly.