On Thermodynamic Universalities and Optics of B-deformed Reissner--Nordström--AdS Black Holes

Abstract

Using machine learning techniques, we study the Reissner--Nordström--AdS black holes in the framework of extended space-time derivatives inspired by non-commutative geometry in string theory where the deformation parameters are related to the inverse of the NS-NS B-field. We refer to these solutions as B-deformed Reissner--Nordström--AdS black holes. Precisely, we examine the thermodynamic and the optical behaviors of such stringy deformed AdS black holes. Exploiting advanced numerical computations, we first examine the corresponding thermodynamic Van der Waals behaviors by calculating the universal ratios describing the P-V criticality and the Joule-Thomson expansion features. Applying such numerical results, we construct reliable training data for a fully connected neural network being developed to determine whether such stringy black hole configurations exhibit thermodynamic Van der Waals aspects. Concretely, we reveal that the fully connected and trained neural network accurately detects Van der Waals behaviors. Supported by the observational data reported by the Event Horizon Telescope international collaborations, we investigate the optical shadows of such B-deformed Reissner--Nordström--AdS black holes using machine learning methods. In order to provide corroborated models, we constraint the involved parameters including the stringy one B by making use of M87* and Sgr A* black hole empirical data.