Null geodesic of Schwarzschild AdS with Gaussian matter distribution

One of the best ways to understand the gravitation of a massive object is by studying the photon's motion 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 and possible motions of the photon are discussed for different energy levels. The nature of the effective potential implies that the photon is prevented from reaching the black hole's center. Different types of possible orbits are considered. A photon with negative energy is trapped in a 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 the possible circular motion of the photon. The closest approach of the photon and the bending angle are also investigated.