The geodesic properties of the hypercylindrical and extraordinary spacetimes

We study the geodesic properties of the two stationary hypercylindrical spacetimes in (4 + 1) dimensions, static and extraordinary spacetime. The effective potential analysis and gravitational lensing effects are studied in the static spacetime. The geodesic equation is numerically solved to get the orbits of light and particles, and we focus on the relation between geodesic orbits and precession rate in the extraordinary spacetime. We give the effective potential and orbits in a specific parameter region. This article was prepared for the proceedings of 11th Italian-Korean Symposium on Relativistic Astrophysics in Korea, Nov. 2009.