1. One of the goals of galactic center black hole observations is the validation of theories of gravity. In addition, recent radio observations have revealed visibility and positional information of light source, and in hte near future we will obtain interferometer observations that will show how the magnetic radiation plasma that surrounds the black hole would be seen by a photographer. Such observations will provide a new tool to study the plasma and spacetime around black hole. Current attempts to verify gravitational theories replace the standard general relativistic Kerr space-time with a perturbed Kerr space-time. Gravitational theories that predict the deviation from general relativity can be included therein. There is a quantum gravity theory which includes the Chern-Simons gravity as an effective theory of gravity other than general relativity. We calculated the observational image of electromagnetic waves from the environs of the black hole by performing accretion simulations using a black hole solution that is predicted by the gravity theory, and perform general relativistic photon radiation transver calculation based on the result. These theoretical calculations in conjunction with future radio interferometry data will provide validation tests for gravitational theories in the near future. The calculated black hole image in the Chern-Simon gravity is different from that of the standard general relativity case, which could possibly be differentiated by future radio interferometry data. We also solve the Teukolsky equation describing the perturbation of the Kerr space-time, and obtain steady-state solutions of the electromagnetic field in the Chern-Simons black hole space-time. 2. To solve the Schrodinger equation for electrons in an electromagnetic field in curved space-time, the analytic solution of Landau levels was obtained. Until now, the analytical solution of the energy levels of electrons containing all quantum effects effects of gravity, the effect of the non-inertial system, and the effect of the electromagnetic field was not known, but in the solution obtained here, all these effects are included for the first time. According to this solution, in addition to the normal Landau quantization, new energy levels appears when the space-time is rotating. Further, the levels found persists even when there is no electromagnetic field, since they are the energy level specific to the space-time rotation. In non-rotating space time, the ambiguity between a proton and electron origin of the Landau levels is a known problem. However, in a rotating space-time, the degeneracy of the origin of Landau levels does not exist. In other words, it can be determined whether protons or electrons are responsible, just by looking at the levels.