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A Conformal Infinity Approach to Asymptotically $$\text {AdS}_2\times S^{n-1}$$ AdS 2 × S n - 1 Spacetimes
Annales Henri Poincaré ( IF 1.4 ) Pub Date : 2020-10-15 , DOI: 10.1007/s00023-020-00958-6
Gregory J. Galloway , Melanie Graf , Eric Ling

It is well known that the spacetime \(\text {AdS}_2\times S^2\) arises as the ‘near-horizon’ geometry of the extremal Reissner–Nordstrom solution, and for that reason, it has been studied in connection with the AdS/CFT correspondence. Motivated by a conjectural viewpoint of Juan Maldacena, Galloway and Graf (Adv Theor Math Phys 23(2):403–435, 2019) studied the rigidity of asymptotically \(\text {AdS}_2\times S^2\) spacetimes satisfying the null energy condition. In this paper, we take an entirely different and more general approach to the asymptotics based on the notion of conformal infinity. This involves a natural modification of the usual notion of timelike conformal infinity for asymptotically anti-de Sitter spacetimes. As a consequence, we are able to obtain a variety of new results, including similar results to those in Galloway and Graf (2019) (but now allowing both higher dimensions and more than two ends) and a version of topological censorship.



中文翻译:

渐近$$ \ text {AdS} _2 \ times ^ {n-1} $$ AdS 2×S n-1时空的共形无穷方法

众所周知,时空\(\ text {AdS} _2 \ times S ^ 2 \)是极值Reissner-Nordstrom解的“近地平线”几何形状,因此,对其进行了研究与AdS / CFT对应关系。受胡安·马尔达塞纳(Juan Maldacena),盖洛韦(Galloway)和格拉夫(Graf)的推测性观点的推动(Adv Theor Math Phys 23(2):403–435,2019)研究了渐近\(\ text {AdS} _2 \ times S ^ 2 \)的刚度满足零能量条件的时空。在本文中,我们基于共形无穷大的概念,采用了一种完全不同且更通用的渐近方法。这涉及对渐近地反de Sitter时空的通常的时态共形无穷大概念的自然修改。结果,我们能够获得各种新结果,包括与Galloway和Graf(2019)相似的结果(但现在允许更高的维度和两个以上的端点)和某种形式的拓扑检查。

更新日期:2020-10-15
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