Null geodesic of Schwarzschild AdS with Gaussian matter distribution

One of the best way to understand the gravitation of a massive object is studying the motion of photon around it. We study the null geodesic of a regular black hole in anti-de Sitter spacetime including a Gaussian matter distribution. Obtaining the effective potential, the possible motions of the photon are discussed for different energy levels. The nature of the effective potential implies that the photon is prevented to reach to the center of the black hole. Different types of possible orbits are considered. A photon with negative energy is trapped in potential hole and has a back and forth motion between two horizons of the metric. However, for specific values of positive energy, the trapped photon still has a back and forth motion, however it crosses the horizons in every direction. The effective potential has an unstable point outside the horizons which indicates on the possible circular motion of photon. The closest approach of the photon and the bending angle are also investigated.