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

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.

arXiv comment24 pages

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Cited by in corpus (4)

• Remarks on the cosmological constant appearing as an initial condition for Milne-like spacetimes
• On the asymptotic assumptions for Milne-like spacetimes
• Topological censorship in spacetimes compatible with $\Lambda >0$
• A lower semicontinuous time separation function for $C^0$ spacetimes