Exact solutions to the geodesic equations of linear dilaton black holes

Abstract

In this paper, we analyze the geodesics of the 4-dimensional linear dilaton black hole (LDBH) spacetime, which is an exact solution to the Einstein-Maxwell-dilaton theory. LDBHs have nonasymptotically flat geometry, and their Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standard Lagrangian method. After obtaining the Euler-Lagrange equations, we show that exact analytical solutions to the radial and angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radial trajectories can be given in terms of the Weierstrass P-function ($\wp $-function), which is an elliptic-type special function.