Critical Phenomena in Anti-de Sitter Black Holes

Abstract

This thesis investigates thermodynamic phase transitions in anti-de Sitter (AdS) black holes. Motivated by the inconsistency of Smarr relation and the first law of black hole thermodynamics in AdS spacetime, cosmological constant L is given a status of thermodynamic variable pressure. This modification has led to the addition of pressurevolume term in the first law of black hole thermodynamics. In this extended phase space, black hole phase behavior is found analogous to everyday physical phenomena. We have focussed our studies on the van der Waals (vdW) like phase transitions and their manifestations, including Joule-Thomson expansion and heat engine in asymptotically AdS black holes. We have chosen charged black hole with a global monopole and a regular Bardeen black hole in AdS spacetime for our study. A detailed study of thermodynamical properties through the Hawking temperature, mass, entropy, heat capacity, and Gibbs free energy is conducted. A first-order phase transition similar to the liquid-gas phase transition is observed between small black hole (SBH) and large black hole (LBH) phases. Critical exponents calculated near the critical point match those of the van der Waals fluid. Further, we investigate the effect of global monopole on the Joule-Thomson expansion (JT) of charged AdS-black holes. We have calculated an exact expression for the JT coefficient, which determines the cooling and heating in the final phase. Using the JT coefficient, we have analyzed the effect of the monopole parameter in the inversion temperature and isenthalpic curves. Similarly, we have extended our studies to regular Bardeen black holes. In another aspect of our study, a heat engine constructed using a black hole as a working substance. The heat engine efficiency is calculated via thermodynamic cycle in the P􀀀V plane, which receives and ejects heat. It is observed that the heat engine efficiency is improved by adding a quintessence field. In the second part of the thesis, we probe the phase structure of the black hole using thermodynamic geometry. Constructing a thermodynamic metric in the phase space, we studied the critical behavior and microstructure of the black hole. Utilizing the analogy with vdW fluid, the thermodynamic geometry of a charged Bardeen AdS black hole is analyzed.