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 at geometry, andtheir Hawking radiation is an isothermal process. The geodesics motions of the test particles are studied via the standardLagrangian method. After obtaining the Euler{Lagrange equations, we show that exact analytical solutions to the radialand angular geodesic equations can be obtained. In particular, it is shown that one of the possible solutions for the radialtrajectories can be given in terms of the Weierstrass P-function (}-function), which is an elliptic-type special function.