Unbound geodesic orbit in the spacetime of charged black hole under higher derivative gravity

Abstract

The unbound orbit of photons and particles in the background of a static spherically symmetric charged black hole spacetime under higher derivative gravity is investigated. By solving the geodesic equations, we have derived the effective potential for the motion of photons and particles. We represent the deflection angle of photons and particles using numerical integration, plot and discuss the unbound orbit of photons and particles. Our calculations indicate that the effective potential for particles is influenced by both the horizon radius and electric charge of the black hole. For black holes with a large horizon radius or a large electric charge, there will always be an extremum in the effective potential. In such a scenario, particles with lower energy moving towards the black hole may experience a repulsive force, leading to their rebound instead of being captured, and due to the presence of repulsion, particles beyond the radius corresponding to the extremum of the effective potential cannot exist in bound orbits.