AdS/CFT对偶的一个应用是通过构造渐近AdS时空来研究与其对偶的强耦合CFT的性质。稳态渐近AdS时空爱因斯坦方程的解比渐近平直时空的情况丰富地多。AdS边界的几何作为边界条件指定，是与其对偶的CFT所在的背景时空。DeTurck方法是近10年来发展起来的求爱因斯坦方程稳态解的方法，它是一种灵活的规范固定的方法，可以将涉及多种边界条件的求稳态时空解问题表述为良好定义的边值问题。本项目以AdS/CFT对偶为理论基础，以DeTurck方法结合谱方法为数值计算技术，求出爱因斯坦方程的稳态渐近(局域)AdS时空解并研究其性质，既是广义相对论中的问题，又为理解强耦合的量子场论提供帮助。拟研究如下体系：AdS边界含黑洞的带电解，对应黑洞背景下的CFT；AdS边界为de Sitter时空的解，用于研究de Sitter时空中的禁闭-退禁闭相变；非平衡稳态解；描述凝聚态体系中平移对称性破缺的解。

According to the AdS/CFT correspondence, general relativity for asymptotically AdS spacetimes sheds some lights on strongly coupled quantum field theories. Significantly more power of AdS/CFT will be unleashed by studying asymptotically locally AdS spacetimes of cohomogeneity-two, in which the geometry depends on both the radial coordinate and another spatial coordinate. The DeTurck method developed in recent 10 years provides a flexible gauge-fixing method for handling various boundary conditions. The following systems are planned to be studied: (1) charged black funnels and droplets, which are dual to CFTs in black hole backgrounds; (2) AdS geometry whose conformal boundary is a de Sitter space; (3) non-equilibrium steady states; (4) holographic models that breaks the translational symmetry describing condensed matter physics.