Phase Transitions and Microstructures of AdS Black Holes

Abstract

The thesis is aimed to understand the aspects of the black hole phase transitions and the underlying microstructures in antide Sitter spacetime. In contrast to the conventional black hole thermodynamics, there exist the thermodynamic variables pressure and volume in the extended thermodynamics approach, which arise from the dynamic cosmological constant. With this utility, we have researched the following things: (i) We used Landau continuous phase transition theory to discuss the van der Waals like critical phenomena of the black hole. The wellknown interpretation of the phase transition of an AdS black hole as being a large and small black hole transition is reinterpreted as being a transition between a high potential phase and a low potential phase. (ii) We probed the phase structure of the regular AdS black holes using the null geodesics. The radius of photon orbit and minimum impact parameter shows a nonmonotonous behaviour below the critical values of the temperature and the pressure, corresponding to the phase transition in extended phase space. The respective differences of the radius of unstable circular orbit and the minimum impact parameter can be seen as the order parameter for the smalllarge black hole phase transition, with a critical exponent 1/2. Our study shows that there exists a close relationship between gravity and thermodynamics for the regular AdS black holes. (iii) We studied the interaction between the microstructures of the HaywardAdS black hole using Ruppeiner geometry. Our investigation shows that the dominant interaction between the black hole molecules is attractive in most part of the parametric space of temperature and volume, as in the van der Waals system. However, in contrast to the van der Waals fluid, there exists a weak dominant repulsive interaction for the small black hole phase in some parameter range. This result clearly distinguishes the interactions in a magnetically charged black hole from that of van der Waals fluid. (iv) By employing a novel Ruppeiner geometry method in the parameter space of temperature and volume, we investigated the microstructure of BornInfeld AdS black hole via the phase transition study, which includes standard and reentrant phase transition. We found that the microstructures of the black hole that lead to standard and reentrant phase transitions are distinct in nature. The critical phenomenon is observed from the curvature scalar, including the signature of the reentrant phase transition.