Investigation of deflection of light phenomena in rotating black hole space-time

Black holes are one of the most interesting and exciting fields of research in modern theoretical physics. The first image of a giant black hole, which has been studied for a long time and is predicted to be located in the center of the M87* Elliptical Galaxy, has brought a new dimension to the research in this area. In this context, there is an increasing interest in both the physical processes in the immediate vicinity of the black holes and the features of the related space-time geometry. In order to deal with the problem of motion around the black hole, it is necessary to know the geometric structure of the related space-time. Because the properties of the movement in question are determined by examining the metric structure of space-time. In this thesis, the geodetic motion of a particle moving in the space-time of rotating black holes is handled and the phenomenon of deflection of light, which is one of the important physical effects in this process, is investigated. The deflection of light phenomenon is one of the most important predictions of General Relativity Theory. This effect has managed to test General Relativity Theory in the weak field. The phenomenon of "gravitational lensing", which is widely studied today in observations of galaxies and galaxy clusters, is one of the most important results of this effect. Kerr-Brane-World black holes, which is the first black hole example that is considered in this thesis; it contains a tidal load in the 5-dimensional membrane-universe model. The Kerr-Brane-World idea is an idea proposed to enable the properties of higher-dimensional gravitation to be examined in 4-dimensions. Investigating the behavior of gravitation in Kerr-Brane-World models, provides a way to adress the physical effects of invisible additional dimensions in our 4-dimensional world. In this thesis, we have also studied Kerr-Kaluza-Klein type rotating black holes. In this kind of black hole solutions, the effect of the 5-dimension in Kaluza-Klein theory is observed with the electric and dilaton charges off Kerr type black holes in 4-dimensional space-time. Our third example is Kerr-Sen black hole which is similar in low-energy string theory to the angular momentum, mass and electric charge parameters in the Kerr-Newman black hole, but is characterized by charges which include dilaton and gauge fields. This black hole solution emerges as the Dilaton-Axion generalization of the Kerr-Newman solution in General Relativity Theory. Within the scope of this thesis, for the test particle, the equations of motions are investigated by Hamilton-Jacobi method and also the effects of the physical parameters contained in the aforementioned metrics on the bending of light are revealed. Additionally, the corresponding angular equations that determine the angle of deflection of light are compared with metric parameters.