The spacetime $AdS_2 \times S^2$ is well known to arise 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. Here we consider asymptotically $AdS_2 \times S^2$ spacetimes that obey the null energy condition (or a certain averaged version thereof). In support of a conjecture of Juan Maldacena, we show that any such spacetime must have a geometry very similar to $AdS_2 \times S^2$ (and under certain circumstances must be isometric to $AdS_2 \times S^2$).

中文翻译：

---

渐近 $AdS_2 \times S^2$ 时空的刚性

众所周知，时空 $AdS_2 \times S^2$ 是作为极值 Reissner-Nordstrom 解的“近视界”几何出现的，因此已经结合 AdS/CFT 对应关系对其进行了研究。在这里，我们渐近地考虑遵守零能量条件（或其某个平均版本）的 $AdS_2 \times S^2$ 时空。为了支持 Juan Maldacena 的猜想，我们证明任何这样的时空必须具有与 $AdS_2 \times S^2$ 非常相似的几何结构（并且在某些情况下必须与 $AdS_2 \times S^2$ 等距）。