Orbits of test particles in three-dimensional Maxwell–Dilaton spacetime: exact analytical solution to the geodesic equation

Abstract

We study the orbits of both massive test particles and light rays in the background of $$(1+2)$$ -dimensional space–time. In particular, we have obtained exact analytical solutions to the geodesic equations in terms of the Weierstras function for the Einstein–Maxwell–Dilaton space–time. The trajectories in the $$(x-y)$$ plane are shown as well, and the comparison with the neutral BTZ space–time is made.