The Applications Of Black Hole Physics:AdS/CFT Duality And Quasi-Normal Modes

This thesis mainly focuses on two directions:AdS/CFT duality and black hole(BH)quasinormal modes(QNMs),both of which are closely related to each other more than the isolation.Especially in holography,the system’s QNMs are dual to the poles of the boundary Green’sfunction,which provides a useful insight for research related to holographic transport and quantum critical phenomena.In the first part of this thesis,we discuss the quantum critical problem in depth using the AdS/CFT duality,including metal-insulator transition,holography butterfly velocity and holographic transport(see Chapter 3).In addition,we also analyze the holographic entanglement entropy(HEE),mutual information and entanglement wedge cross-section(EWCS)in the system with the zero entropy density at the ground state(see Chapter 4).Particularly,we adequately introduce the background knowledge,motivation and research significance in Chapter 2.we also exhibit the methodology for more specific computation and the basic information of the holographic theory,they will be set as the prelude on each chapter,to provide the reader with a comprehensive understanding of the overall background research.Therefore,the reader is able to gain a clear understanding of the physical starting point and corresponding calculations by integrating knowledge from the background information presented in each chapter.In the second part,we discuss properties of QNMs in a charged Weyl black hole and a loop quantum gravity black hole(see Chapter 5).The preface of Chapter 5 mainly presents the conceptual framework of BH QNMs and its intimate connection with gravitation waves(GWs).then we discuss the QNM properties in different two types of BH model.While in Chapter 6,we show our conclusions and prospects.The quantum phase transition(QPT)is a topic that has garnered significant and sustained attention in the field of condensed matter physics.Research into QPT can provide us with a profound understanding of fundamental properties of matter,such as high-temperature superconductivity,as well as the quantum information theorem that describes long-range interactions.However,the strong correlation may prevent us from using a normal perturbation procedure to make calculations on QPT.Until the proposal of AdS/CFT,this situation was completely overturned.Based on AdS/CFT duality,we can describe the boundary CFT by using the classical gravitational theory in the bulk.This provides a new path to deal with the strong correlated QPT problem.In the frame of holography,we first study the relationship between the strong correlated QPT and the holographic butterfly velocity.In holography,The emergence of the quantum phase transition is commonly associated with the change of the infrared(IR)geometry.Therefore,the property of holographic butterfly velocity is purely determined by IR geometry.One can conjecture that the holographic butterfly velocity must have an intimate relationship with the holographic quantum phase transition.Following this point,we systematically study the phase structure of the Einstein-Maxwell-Dilaton-Axions(EMDA)model and the behavior of butterfly velocity in different phases.We found that the system exhibits a metal-insulation transition depending on the parameters of the holographic theory.Meanwhile,the butterfly velocity and its first derivative exhibit a local extreme near the quantum critical point,which means that the butterfly velocity can diagnose the occurrence of the QPT and agrees with the condensed matter theory(CMT).Further,the scaling behaviors of the butterfly velocity confirm the connection between the phase transition and the IR geometry.Especially,we also find a novel quantum phase transition in the case of γ=9/2,which prompts us to do a further study of the transport properties for this case.An obvious characteristic is that a normal metal phase(with AdS2 IR geometry)supports a Drude peak in the low frequency region,indicating a coherent system.While in the novel metal phase(with an IR geometry of hyperscaling violation),AC conductivity at the low frequency region becomes slow,which corresponds to an incoherent system.Furthermore,we find that the incoherent behavior becomes stronger when the strength of the momentum dissipation increases.Next,we study the information property of the system with the zero entropy density at the ground state(see chapter 4).Compared to the on-vanishing ground state entropy density system,the research on the system with zero ground state entropy density can help us understand the universal properties of the real system and also help to study the mixed-state entanglement.Firstly,we compute the HEE of the Gubser-Rocha model,and find a peculiar property in this model:in the low-temperature region,the HEE decreases with the temperature increase,which is contrary to that in most holographic models.We argue that this novel phenomenon results from the singular property of the Gubser-Rocha model in the limit of zero temperature,and provides an analytical proof for our guess.In addition,we also study the mutual information and EWCS,and compare it with a non-vanishing ground-state entropy density system,i.e.,the RN-AdS black hole.Our results indicate that the HEE and MI are always the bigger ones in the Gubser-Rocha model,but it behaves inversely in the case of EWCS.This may implies that the mixed-state entanglement entropy would have a better description in EWCS.Finally,we study the properties of QNMs in two different kinds of BH,respectively,which contains a charged Weyl black hole(see section 5.3)and a loop quantum gravity black hole(LQG-BH)(see section 5.3).The study on QNMs can help us to theoretically analyse the gravitational waves,such as the information of the residue from the combination of binary stars,and the examination the no-hair theorem.In our work,we find that the imaginary part of QNMs is always negative;this means the system is stable under the scalar field perturbation.We also compute the Hawking radiation for this model,and that result is consistent with the behavior of the QNMs.While for this peculiar Weyl gravity model,we notice that the late tail stage of the time evolution emerges exponential decay.On the other hand,for the LQG-BH,we investigate the QNMs and compare it with the Schwarzschild black hole(SS-BH).We can find that the loop quantum effect influences the behaviors of the high overtone of QNMs,and such an anomalous phenomenon results in the oscillation of the scalar field in the LQG-BH to be nearly identical to that in the SS-BH.Therefore,the high overtone modes in LQG-BH play an important role,which is expected to be detected by future observations.