Equatorial Circular Orbits of Neutral Test Particlesin Weyl Spacetimes

A general stability study of equatorial circular orbits in static axially symmetric gravitating systems is presented. We investigate the motion of neutral test particles in circular geodesics such as the marginally stable orbit, the marginally bounded orbit, and the photon orbit are analyzed. We find general expressions for the radius, specific energy, specific angular momentum, and the radius of the marginally stable orbit, both for null and timelike circular geodesics. Different solutions were expressed in different coordinates systems: cylindrical coordinates, oblate spheroidal coordinates, and prolate spheroidal coordinates are considered. We show that all null circular trajectories are unstable, and that there aren't marginally stable null geodesics, whereas for timelike geodesics the motion can be unbounded, bounded, or circular.