The Bulk-Boundary Correspondence for the Einstein Equations in Asymptotically Anti-de Sitter Spacetimes.
The Bulk-Boundary Correspondence for the Einstein Equations in Asymptotically Anti-de Sitter Spacetimes.
复制标题
爱因斯坦方程在渐近抗DE的平稳期间的散装对应关系。
DOI：
10.1007/s00205-023-01890-9
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发表时间：
2023
影响因子：
2.5
通讯作者：
中科院分区：
文献类型：
--
作者：
本文考虑具有共形边界的真空渐近反de Sitter时空。我们建立了一个对应，近，这样的时空和它们的共形边界数据。更具体地说，给定一个域，我们证明了系数和（待定项，或应力能量张量）在一个费曼-格雷厄姆扩展的度量g从边界唯一确定g附近，提供满足广义零凸性条件（GNCC）。GNCC是上的共形不变准则，首先由Chatzikaleas和第二作者确定，它确保了pseudoconvex超曲面在附近的叶理，并且在极限处退化。作为这一结果的推论，我们推导出满足GNCC的域的共形对称性扩展到附近的时空对称性。证明，这不需要任何解析性假设，依赖于三个关键成分：（1）为这种设置开发的垂直张量场的微积分;（2）一个新的系统的运输和波动方程的差异的度量和曲率量;（3）最近建立的Carleman估计张量波动方程附近的共形边界。
In this paper, we consider vacuum asymptotically anti-de Sitter spacetimes with conformal boundary . We establish a correspondence, near , between such spacetimes and their conformal boundary data on . More specifically, given a domain , we prove that the coefficients and (the undetermined term, or stress energy tensor) in a Fefferman–Graham expansion of the metric g from the boundary uniquely determine g near , provided satisfies a generalised null convexity condition (GNCC). The GNCC is a conformally invariant criterion on , first identified by Chatzikaleas and the second author, that ensures a foliation of pseudoconvex hypersurfaces in near , and with the pseudoconvexity degenerating in the limit at . As a corollary of this result, we deduce that conformal symmetries of on domains satisfying the GNCC extend to spacetime symmetries near . The proof, which does not require any analyticity assumptions, relies on three key ingredients: (1) a calculus of vertical tensor-fields developed for this setting; (2) a novel system of transport and wave equations for differences of metric and curvature quantities; and (3) recently established Carleman estimates for tensorial wave equations near the conformal boundary.
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影响因子：
1.7
作者：
Alexakis, Spyros;Schlue, Volker;Shao, Arick
通讯作者：
Shao, Arick
影响因子：
2.4
作者：
Chatzikaleas, Athanasios;Shao, Arick
通讯作者：
Shao, Arick
影响因子：
1.5
作者：
FRIEDRICH, H
通讯作者：
FRIEDRICH, H
影响因子：
2.4
作者：
Alexakis, S.;Ionescu, A. D.;Klainerman, S.
通讯作者：
Klainerman, S.
影响因子：
2.5
作者：
Enciso, Alberto;Kamran, Niky
通讯作者：
Kamran, Niky