Geodesics of Black Holes in Bumblebee Gravity Theory

In this thesis, our main purpose is to study the geodesics of bumblebee black hole (BBH) in 4-dimension (4D), which is an exact solutions to the bumblebee gravity theory. The motions of photon and massive particles are going to be studied via the standart Lagrangian method in asymptotically flat geometry. Due to the physical constraints, instead of spacelike geodesics, we concantrate on null and timelike solutions. After finding the Euler Lagrange equations, next step is invastigating radial motions of geodesics. Moreover, exact analytical solutions are also planned to be studied for the radial and angular geodesic equations. According to our purpose, we use some numerical simulations in order to plot graphs for visualizing the geodesics. We also investigate the limit of Lorentz symmetry breaking term (LSB) by using classicsal tests which are the advance of the perihelion and bending of light. Keywords: General Relativity, Standart Model Extensions, Bumblebee Gravity Theory, Black Hole, Geodesics, Perihelion, Lorentz Symmetry Breaking, Deflective Angle.