Black Hole Phase Transition And Quasi-normal Modes

The discovery of Hawking radiation solves the contradiction in the thermodynamics of black holes,but also implies the internal relation among gravity,thermodynamics and quantum mechanics.Recently,the research shows that there is a correspondence between Hawking radiation and quasi-normal modes.Moreover,the development of black hole thermodynamics also reveals more and more deeply the internal relations between quantum theory,thermodynamics and gravity theory.Studies of thermodynamic properties of AdS black holes begin with the seminal paper of Hawking and Page,which demonstrated the existence of a certain phase transition at a fixed temperature in the phase space of Schwarzschild-AdS black hole.Among the ideas,cosmological constant can be interpreted as a pressure in an asymptotically AdS black hole space time in a thermodynamic sense.Recently,many efforts have been devoted to study about this.In this paper,we will mainly discuss the Hawking radiation,quasi-normal modes and Hawking-Page phase transition,and present the work we have made in these topics.Firstly,we apply the effective framework of non-strictly thermal to large AdS black holes in different dimensions.We introduce the effective temperature and show that the effective mass is approximatively the average one in any dimension.Through Hawking radiation-quasinormal modes correspondence we calculate the Bekenstein-Hawking entroy,the horizon area quantization,the area quanta number,and the number of microstates.Then,we investigate the influence of the Hawking-Page phase transition on Hawking radiation.The results show that the tunneling emission probability suffers a sudden change accompanied when the Hawking-Page phase transition occurs.Finally,we explore the possible microscopic structure of a charged AdS black hole from the quantized viewpoint.By the quantization of the black hole horizon area,we show the relation between the number of quanta of area and the microscopic degrees of freedom of the black hole.Then we also interpret a latent heat of thermodynamical phase transition as a transition between the number of quanta of area of large black hole(LBH)and the number of quanta of area of small black hole(SBH)in the charged AdS black hole.Moreover,the Ruppeiner scalar curvature connecting with the number of quanta of area is also shown.