A Conformal Infinity Approach to Asymptotically $$\text {AdS}_2\times S^{n-1}$$AdS2×Sn-1 Spacetimes

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.