Geodesic behavior of charged black hole in AdS spaces with Reissner–Nordstrom–AdS metric

In this work, we introduce an electric charge in anti-de Sitter (AdS) space with a Reissner–Nordstrom–AdS black hole. The primary purpose of the present work is to review and describe the time-like and null geodesic behavior of the black hole. Here, we analyze the lapse function in order to gain some insights about the event horizon of the black hole and the geometrization of the space–time. We also present black hole horizons in 3D form. To have a deeper understanding of the motions of photon-like and massive particles in black hole gravity, we have derived some types of effective potentials. We have also examined the effect of variation of Newtonian constant G in almost every case, which allows us to identify gravity’s nature and its role in the structure of the universe. Finally, we give the Lyapunov exponent for orbital balance for familiarization with it and found that the stability of the circular orbit of the particle moving in the field of gravitation of black hole is conditional and the condition of stability of the orbit is 4 Q 2 − 9 GM 2 ⩾ 0 and G > 0.