Study On The Atom Self - Excitation Problem Of AdS Black - Hole Phase Transition And High - Dimensional Black Hole

It was almost half a century since the black hole thermodynamics was explored. As a theo-ry of researching the quantum effort in the strong gravitational field, it strongly suggests that gravitational theory, quantum theory and thermodynamics have a profound and fundamental relationship between each other. As we known, phase transition is an important concept in ther-modynamics. In terms of the AdS/CFT correspondence, the AdS black hole phase transition under different background has been investigated deep and widely. Therefore, the first focus in this thesis is the critical behavior of the black holes with negative cosmological constan-t. Meanwhile, hawking radiation is also an important effort in black hole thermodynamics, which has been researched by many methods. In order to understand this quantum effort in strong gravity better, we use DDC formalism to study the heating effect of the higher dimen-sional spacetime impact on the radiation properties of the two-level atom, which is the second focus in this thesis.Firstly we introduce the background and structure of this thesis. We also emphasis the physical motivation and feasibility of this thesis. In Chapter 2, we introduce the research method of the criticality of the AdS black hole. Then in the following Chapter 3 we study the P—V critical behavior of a four-dimensional AdS black hole in an Einstein-Maxwell gravity with a conformal anomaly by treating the cosmological constant as a variable that is related to the thermodynamic pressure. It is shown that there will be phase transition if the cur-vature is positive. When the charge of the conformal field and the coefficient satisfy a certain relation, the van de Waals like phase transition for the spherical black hole can occur where the temperature is lower than the small critical temperature or higher than the large one. We also evaluate the critical exponents of the phase transitions and find that the thermodynamic exponents associated with this four-dimensional AdS black hole coincide with those of the van de Waals fluid. The results show the conformal anomaly term brings richer phase structures and critical behavior than that of a RN-AdS black hole.In Chapter 4, we study the P-V critical behavior of N-dimensional AdS black holes in Einstein-Maxwell-power-Yang-Mills gravity. Our results show that when the power of the nonlinear Yang-Mills field and the dimension of the spacetime satisfy the different relations, the solution of the black hole will be separated into two branches. We find that in the first branch the critical behavior will exist under some special constraint condition of the charge of Maxwell and Yang-Mills field and the dimension of spacetime. In the second branch, the critical behavior always exist without any constraint condition. We also find that there is at most one critical point in the system. We have also calculated the critical exponents at the critical point and found in all cases the critical exponents coincide with those of the Van der Waals fluid. Finally, both of the Ehrenfest’s equations have been verified to hold at the critical point, which shows that in resemblance with the liquid-gas phase transition, the phase transition of the EMPYM black hole at the critical point is of the second order.In Chapter 5, we investigate the spontaneous excitation of an static atom interacting with electromagnetic vacuum fluctuations outside a EGB black hole in d-dimensions by using the generalized DDC formalism. We examine free quantum electrodynamics in static spherically symmetric spacetime of arbitrary dimensions in a modified Feynman gauge. We give all of the physical modes functions which consummate the results in Ref. It shows that spon-taneous excitation does not occur in Boulware vacuum, while exists in Unruh vacuum and Hartle-Hawking vacuum. As to the total rate of change of the atomic energy, it does not receive the contribution from the coupling constant of Gauss-Bonnet term at spatial infinity, only the dimensional parameter has the contribution to it. Near the event horizon, the coupling constant and the dimension p both have contribution to the total rate of change of the atomic energy in all three kinds of vacuum. We discuss the contribution of the coupling constant and dimensional factor to the results in three different kinds of spacetime in the last.