Phase transition in black holes

The present thesis is devoted towards the study of various aspects of the phase transition phenomena occurring in black holes defined in an Anti-de-Sitter (AdS) space. Based on the fundamental principles of thermodynamics and considering a grand canonical framework we examine various aspects of the phase transition phenomena occurring in AdS black holes. We analytically check that this phase transition between the smaller and larger mass black holes obey Ehrenfest relations defined at the critical point and hence confirm a second order phase transition. This include both the rotating and charged black holes in Einstein gravity. Apart from studying these issues, based on a canonical framework, we also investigate the critical behavior in charged AdS black holes. The scaling laws for these black holes are found to be compatible with the static scaling hypothesis. Finally, based on the usual framework of AdS/CFT duality, we investigate the phase transition phenomena occurring in charged hairy black holes defined in an asymptotically AdS space. Based on analytic calculations, and using the AdS/CFT dictionary, we explicitly compute the order-parameter for the dual CFT close to the critical point of the phase transition and found that the critical exponent associated with the condensation is $\frac{1}{2}$, which is the universal result of the mean field theory. Moreover, we also find that in the presence of an external magnetic field, the dual CFT exhibit a perfect diamagnetism at low temperatures, which may be regarded as the reminiscent of the so called Meissner effect