Scalar Quasinormal Modes And P-wave Superconductors In Certain Asymptotically AdS Spacetimes

With the proposal of holographic principle and the implementation of Ad-S/CFT correspondence,the scalar hairs of black holes that exist at low tem-peratures and disappear at high temperatures are discovered by considering the complex scalar field coupled to the Einstein-Maxwell theory.The way to solve the equations of hairy black holes of this kind is by numerically integrating out from the horizon to infinity.The key to the emergence of the scalar hair is to set the source of the dual operator to zero according to the AdS/CFT correspondence.The characteristic of the scalar hairs that exist at low temperatures and disappear at high temperatures,is realized by introducing a scale to obtain the expectation value of the charged scalar field which changes with temperature at a fixed charge density.On the one hand,this phenomenon is related to the phase transition of super-conductors in condensed matter physics.It is hoped that the study of holographic superconductors can play a guiding role in the related research in condensed matter physics.And different holographic superconducting models have been established through choosing different AdS black holes as backgrounds,and the holographic properties of AdS black holes therefore have been extensively studied.On the oth-er hand,the appearance of the scalar hair provides more evidence that the black hole does not necessarily satisfy the no-hair theorem.Regarding the breakdown of the no-hair theorem,in fact,in Bekenstein's previous work,people have realized that the solution of the Einstein equation with the coupled scalar field can avoid the standard no-hair theorem.Later,people extended this kind of solution with the coupled scalar field to the case with a cosmological constant.Recently,large classes of new hairy AdS black hole solutions have been found by considering the coupled scalar field.This dissertation mainly studies the holographic properties of the new AdS black hole with the coupled scalar field,as well as its stability under the massless scalar field perturbations.First,we study the planar AdS black hole solutions in a particular Lovelock theory with the nonminimally coupled self-interacting scalar field,and indexed by an integer k.On the one hand,k is closely related to the nonminimal coupling pa-rameter.The physical meaning of the nonminimally coupled scalar field is that it may cause black holes to form hairs other than mass7charge and angular momen-tum.In fact,when a thermodynamic study on this kind of black hole solution was performed,it was found that there is an integral constant that is completely inde-pendent of other conserved charges and is interpreted as a new "hair".On the other hand,such solutions are only valid when k?2.since the existence of these solu-tions stems from the existence of higher-order curvature terms of Lovelock gravity.We study the properties of holographic superconductors in five-dimensional and six-dimensional black hole backgrounds by using Maxwell-vector p-wave model,and discuss the influence of the parameter k on the conductor/superconductor phase transition.It is found that the larger the k,the lower the critical tem-perature,then the more difficult the phase transition is.At the same time,we calculated the energy gap which changes with the metric parameter k,tempera-ture,mass of vector field.In addition,by applying a scalar field perturbation to the black hole,we study the stability of this black hole and discuss the effect of the parameter k on the quasinormal modes.We find that due to the existence of the coupled scalar field in background,the nature of the quasinormal modes is changed,where the real part of the quasinormal modes frequency is zero,however the black hole eventually returns to the equilibrium state.In addition to the black hole found in the particular Lovelock theory men-tioned above.There is another class of hairy AdS black hole solutions,which is found in the Einstein-scalar theory by considering Einstein gravity nonminimally or minimally coupled to a scalar field with a given potential.In this case,it has a more concise mathematical form and can restore to the Schwarzschild-AdS black hole under the condition of metric parameters taking limiting values.We construct the Maxwell-vector p-wave model by using this hairy AdS black hole,and study the characteristics of conductor/superconductor phase transition in dual systems.By comparing with the results of Schwarzschild-AdS,the influence of the scalar hair in the background on the vector field condensation is discussed.It turns out that in the condition of the probe limit where the backreaction of the space-time is neglected,as we reduce the temperature to a critical value,the black hole appears unstable and forms a vector hair.Moreover,due to the existence of the coupled scalar field in background,the condensation of the vector field is easier.