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.

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。