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It is well known that the spacetime $\text{AdS}_2\times S^2$ arises as the`near horizon' geometry of the extremal Reisser-Nordstrom solution, and forthat reason it has been studied in connection with the AdS/CFT correspondence.Motivated by a conjectural viewpoint of Juan Maldacena, the authors in [4]studied the rigidity of asymptotically $\text{AdS}_2\times S^2$ spacetimessatisfying the null energy condition. In this paper, we take an entirelydifferent and more general approach to the asymptotics based on the notion ofconformal infinity. This involves a natural modification of the usual notion oftimelike conformal infinity for asymptotically anti-de Sitter spacetimes. As aconsequence we are able to obtain a variety of new results, including similarresults to those in [4] (but now allowing both higher dimensions and more thantwo ends) and a version of topological censorship.

A conformal infinity approach to asymptotically $\text{AdS}_2\times S^{n-1}$ spacetimes