Abstract
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 for
that 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 $\text{AdS}_2\times S^2$ 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 [4] (but now allowing both higher dimensions and more than
two ends) and a version of topological censorship.