Real particle geodesics and thermodynamics of a black hole in regular Schwarzschild–Anti-de Sitter spacetime

Regular Schwarzschild–Anti-de-Sitter (RSch–AdS) spacetime, a non-rotating, non-charged maximally symmetric and Lorentzian manifold of negative curvature, is a solution of Einstein’s field equations with a negative cosmological constant and a matter source of a Gaussian distribution. Characteristics of a black hole (BH) in such a spacetime, known as RSch–AdS-BH, can be instructive from various aspects and lead to a better understanding of it. In this regard, geodesics of real particles around RSch–AdS-BH and RSch–AdS thermodynamics of BH are two important and motivating issues that we are going to evaluate in this research. For this purpose, we first obtain the geodesics of real particles numerically based on initial values and boundary conditions such as mass distribution, angular momentum and cosmological constant and interpret their behavior. Second, we are interested in investigating a BH in the RSch–AdS spacetime from a thermodynamic point of view and comparing some of its aspects such as temperature, entropy, heat capacity and Gibbs free energy with the corresponding asymptotic spacetime (Sch-AdS). We underscore that results obtained in RSch–AdS spacetime, a noncommutative geometry based on uncertainty principle of quantum gravity and Gaussian distribution of mass, are more accurate and therefore the superiority of this model is more considerable.