Geodesic structure of the Clifton-Barrow black hole space-time

In this paper, we investigate the geodesic structure of Clifton-Barrow black hole space- time. Through the numerical analysis of the effective potential and the motion equation, the orbital types of test particles and photons and the corresponding orbital motion diagrams of each orbital types under certain conditions are obtained. We find that angular momentum b and delta determine the existence of bound orbits and circular orbits. And we also find that the radius of unstable circular orbit decreases with increases in b while the radius of stable circular orbit increases. Furthermore, as delta increases, the radius of unstable circular orbit increases, while the radius of stable circular orbit decreases. For null geodesic, parameters b and delta do not affect the types of null orbits. The radius of the unstable circular orbits increases with the increase of delta. However, the radius of the unstable circular orbits remains unchanged as b increases. Also, we show that the precession direction of the bound orbits of the test particles is counterclockwise for b = 2.15, but clockwise with b = 3.6. Moreover, different energy values have an effect on the curvature of escape and absorb orbits curve.