Measuring the parameters of supermassive black holes from space

To describe black hole in astrophysics typically astronomers use Newtonian approaches for gravitational field because usually one analyzes processes acting far enough (in Schwarz- schild radius units) from black hole horizons. Here we discuss phenomena where we have to use general relativistic approaches to explain present and future observational data like Fe Kα line profiles and shapes of shadows around black holes. Different X-ray missions such as ASCA, XMM-Newton, Chandra etc. discovered features of Fe Kα lines and other X-ray lines as well. Attempts to fit spectral line shapes lead to conclusions that sometimes the profiles line shapes should correspond to radiating regions which are located in the innermost parts of accretion disks where contributions of general relativistic phenomena are extremely important. As an illustration we consider a radiating annulus model to clarify claims given recently by Mu ̈ller & Camenzind (2004). We discuss properties of highly inclined disks and analyze a possibility to evaluate magnetic fields near black hole horizons. We mention also that shadows could give us another case when one could evaluate black hole parameters (namely, spins, charges and inclination angles) analyzing sizes and shapes shadows around black holes. We discuss glories (mirages) formed near rapidly rotating Kerr black hole horizons and propose a procedure to measure masses, charges and rotation parameters analyzing these forms of mirages. We also propose to use future radio interferometer RADIOASTRON (Millimetron or MAXIM) facilities to measure shapes of mirages (glories) and to evaluate the black hole spin as a function of the position angle of a distant observer. We propose also a procedure to measure a black hole charge with future space missions.