Geodesics of Linear Dilaton Black Holes

In this thesis, we investigate the geodesics of the 4-dimensional (4D) linear dilaton black hole (LDBH), which is an exact solution to the Einstein-Maxwell-Dilaton (EMD) theory. These spacetimes have non-asymptotically flat (NAF) geometry. The motions of massless (null) and massive particles (timelike) are studied via the standard Lagrangian method. Due to the physical necessities, we do not consider the spacelike geodesics. After obtaining the Euler-Lagrange (EL) equations, we separately analyze both radial and circular motions of those geodesics. In the same line of thought, we perform numerical simulations in order to plot many graphs for displaying the geodesics. Exact analytical solutions are also obtained for the radial and the angular geodesic equations. In particular, it is shown that the radial trajectories are governed by the WeierstrassP-function (-function), which is an elliptic-type special function. Keywords: Linear dilaton black hole, Geodesics, WeierstrassP-function.