Some thermodynamics aspects in Regular Gaussian Black Hole

Asymptotically Anti-de Sitter (AdS) Black Hole (BH) space-times are of theoretical and mathematical interest and attractive. On the other hand, in the last few decades, the theory of regular (nonsingular) BHs has gained many researchers and enthusiasts. Therefore, space-times asymptotically AdS and free of (essential) singularities can have a double attraction. An example of such space-time is the Regular Gaussian Black Hole (RGBH). In this paper, some thermodynamical properties of this BH are studied and examined through the calculation of thermodynamic functions and related diagrams. The results of the calculations and related diagrams indicate that a background AdS space-time is more compliant with the laws of the physical world than a de Sitter (dS) one. Finally, with a brief discussion about Geometrothermodynamics, it is clear that the space-time structure of RGBH supports the fundamental relationship between gravity, thermodynamics and quantum theory.