高阶引力修正下AdS黑洞的热力学性质及其相关问题研究

AdS时空黑洞具有丰富的相结构与热力学性质，同时AdS/CFT对偶作为研究强耦合凝聚态系统的有力工具，使得AdS时空黑洞热力学及其相关问题的研究备受关注。本项目拟在已有工作基础上，围绕AdS时空黑洞开展以下工作：利用等面积定律和相变理论对高阶引力背景下AdS黑洞相结构和临界热力学行为进行深入研究；利用二流体模型对黑洞微观结构以及黑洞分子的实质进行探讨；利用AdS时空黑洞构建强耦合凝聚态系统拓扑超导体的全息模型，对反作用、磁场作用下拓扑超导体组成的约瑟夫森结界面处的无耗散边界电流等效应进行深入研究；考虑在高阶引力修正下手征无耗散边界电流的相关特性以及普适关系。项目的开展有助于加深对AdS时空黑洞热力学性质及黑洞熵本质的理解，为量子引力理论的建立提供理论支持，也会为理解强耦合凝聚态系统提供有力的帮助。

The AdS spacetime black holes have abundant phase structures，and AdS/CFT duality is a powerful tool for the study of strongly coupled condensed matter systems，and asymptotically As a result, the research on the thermodynamics of AdS space-time black hole and its related problems has attracted much attention. Based on the existing work, the following research topics will be carried out around AdS space-time black hole. We will study that the phase structure and critical thermodynamic behavior of AdS black hole under high order gravity by using the laws of equal area and the theory of phase transition. We will investigate the black hole microstructure and the black hole molecules by using the two-fluid model. Using AdS space-time black hole we will construct the holographic model of topological superconductor in a strongly coupled condensed matter system. We will study the chrial edge currents and the physical properties of the topological Josephson junctions by considering the backreaction to the metric background and the added magnetic field. Considering the effect of higher curvature, we will study the physical properties of the topological Josephson junctions and the properties of spontaneously generated edge currents. The implementation of the project will help to further understand the thermodynamics of AdS space-time black holes and the nature of black hole entropy, provide theoretical support for the establishment of quantum gravity theory, and deepen the understanding of strongly coupled condensed matter systems.