Study Of Thermodynamics And Phase Transition Of AdS Black Holes

The thermodynamics of black holes shows that the essence of black hole system is a quantum system.The qualities of black hole,such as entropy,temperature,and holography of gravity provide an important window for quantum gravity study.We can get a deep insight of quantum gravity and other important research area through the study of black hole thermodynamics.In the extended phase space,where we treat the cosmological constant as a thermodynamic pressure,we investigated the critical behavior of d-dimensional singly spinning Kerr Anti de Sitter(AdS)black hole and Kerr-Newman AdS black hole systems.First of all,we introduced the course of development and theoretical foundation of black hole thermodynamics in the first chapter.The primary motivation of studying asymptotically AdS black holes is the AdS/CFT correspondence,which asserts a dual relationship between a d-dimensional AdS space to a Conformal Field Theory(CFT)formulated on its(d-1)-dimensional boundary.However,in the extended phase space as the cosmological constant ?=(d-1)(d-2)/(2l2),where l is the AdS radius,plays a role in thermodynamics system rather than a background constant,there should be a thermodynamic quantity on boundary dual to the bulk pressure P,i.e.l In the first chapter,we surveyed recent development on black holes thermodynamics and AdS/CFT correspondence.Secondly,the d-dimensional singly spinning Kerr AdS black holes exhibit the van der Waals phase transition and reentrant phase transition.Since the black hole system is a single-characteristic-parameter system,we show that the form of the critical point can be uniquely determined by the dimensional analysis.When d = 4,we get the analytical crit-ical point.The coexistence curve and phase diagram are obtained.The result shows that the fitting form of the coexistence curve in the reduced parameter space is independent of the angular momentum.When (9 = 5 ? 9,the exact critical points are numerically solved.It demonstrates that when (9 ? 6,there are two critical points.However,the small one does not participate in the phase transition.Moreover,the exact critical reentrant phase transition points are also obtained.All the critical points are obtained without any approximation.What's more,as for the critical behavior of Kerr-Newman Ad S black hole system,the critical points for the van der Waals like phase transition are numerically solved.The highly accurate fitting formula for them is given and is found to be dependent of the charge and angular momentum .In the reduced parameter space,we find that the temperature,Gibbs free energy,and coexistence curve depend only on the dimensionless angular momentum-charge ratio = /2rather than and .Moreover,when varying from 0 to ?,the coexistence curve will continuously change from that of the ReissnerNordstr¨om-Ad S black hole to the Kerr-Ad S black hole.These results may guide us to study the critical phenomena for other thermodynamic systems with two characteristic parameters.Finally,we made a conclusion and outlook in the last chapter.We reviewed our results and deficiencies of our works,and made a outlook of future direction.