论文标题
爱因斯坦 - 维库姆的近边界几何形状渐近地抗DE的平稳时代
The Near-Boundary Geometry of Einstein-Vacuum Asymptotically Anti-de Sitter Spacetimes
论文作者
论文摘要
我们研究了一般的渐近抗DE保姆空间的几何形状，靠近共形边界。特别是，时空仅被认为具有有限的规律性，并且可以具有任意的边界拓扑和几何形状。对于主要结果，我们在各种几何量的共形边界处得出限制，并使用这些限制来构建部分Fefferman-Graham扩展从边界扩展。本文的结果将在即将到来的论文中应用于证明对称性扩展和重力 - 结合对应的定理，用于渐近抗DE的真空平台。
We study the geometry of a general class of vacuum asymptotically Anti-de Sitter spacetimes near the conformal boundary. In particular, the spacetime is only assumed to have finite regularity, and it is allowed to have arbitrary boundary topology and geometry. For the main results, we derive limits at the conformal boundary of various geometric quantities, and we use these limits to construct partial Fefferman--Graham expansions from the boundary. The results of this article will be applied, in upcoming papers, toward proving symmetry extension and gravity--boundary correspondence theorems for vacuum asymptotically Anti-de Sitter spacetimes.
