引力和黑洞的全息性质是上世纪末期理论物理学中最重要的认识之一，特别是在发现引力全息性的第一个具体实现——AdS/CFT之后，关于一般的规范/引力对偶及其应用的研究成为持续多年的热点方向。近年来，相关研究又出现了一些非常重要的进展，特别是刘洪等人关于全息超流模型在量子湍流研究中的贡献，以及规范/引力对偶在描述更实际的非均匀强耦合体系、研究强耦合体系的非平衡稳态和更一般动力学过程中的应用等，而这些进展越来越实质地依赖于数值方法。有鉴于此，本研究项目主要关注数值相对论在这一交叉领域的应用，涉及以下方面的内容：一般规范/引力对偶体系（带反作用）的动力学及其数值模拟；全息超流体系中不同类型量子湍流的产生、性质和层流-湍流转变；规范/引力对偶体系的稳定性和准正模式、输运性质和膜方法；规范/引力对偶的其它数值和理论研究课题。期望该项目的研究能够通过数值方法的发展将规范/引力对偶及其应用推向一个新台阶。

The holographic property of gravity and black holes is one of the most important knowledges in theoretical physics we learned in the end of the last century. Especially, after the discovery of AdS/CFT, the first concrete realization of this holographic property, research works concerning the general gauge/gravity duality and its applications have become the long lasting hot field in theoretical physics. During the recent years, there are some significant developments in related researches, among which the application of the holographic superfluid model to the study of quantum turbulence by Hong Liu et al is of special interest, as well as other applications of gauge/gravity duality to describe more realistic inhomogeneous and strongly coupled systems and to study the steady states and more general dynamical processes of strongly coupled systems, etc. Needless to say, these developments more and more essentially rely on numerical methods. Based on this ground, this research project mainly focuses on the applications of numerical relativity to this inter-discipline field, including the following aspects: dynamics (with back-reaction) of the general gauge/gravity systems and its numerical simulation; generation, properties of various types of quantum turbulence and quantum laminar-turbulent transition; stability and quasi-normal modes, and transport properties and membrane paradigm of gauge/gravity systems; other numerical and theoretical subjects on the gauge/gravity duality. Hope that this project can push the study of gauge/gravity duality and its applications to a higher level via the development of numerical methods.