The thesis explores the thermodynamics of various black holes within the AdS (Anti-de Sitter) spaces. Initially, we examine their temperature, entropy, and mass relations, and eva‎luate the heat capacity to analyze the phase structure of these black holes. Utilizing the first law of thermodynamics, we can express the specific heat capacity as the second derivative of energy. By definition, the existence of a discontinuity in the secondorder derivative of energy results in a second-order phase transition within the thermodynamic system. These specific points where the specific heat capacity exhibits discontinuity are referred to as ”Davis points.” Based on specific conditions that we establish, Davis points are classified into two categories: Davis points type 1 and Davis points type 2. Davis points type 2 are also known as critical points. Additionally, we investigate the thermodynamic topology of these black holes using a novel approach. The first step involves reviewing the thermodynamic topology based on the introduced potential, where the topological charge at critical points is interpreted as phase creation and annihilation points. Subsequently, to compute the topological charge of all Davis points within a thermodynamic system, we introduce a novel potential and proceed to restructure and investigate the thermodynamic topology. This will result in the introduction of a new concept for topological charge.

بهروز ميرزا

احمد شيرزاد

صديقه سجاديان , مسلم زارعي