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# Advances in Theoretical and Mathematical Physics

## Volume 23 (2019)

### Number 2

### Rigidity of asymptotically $AdS_2 \times S^2$ spacetimes

Pages: 403 – 435

DOI: https://dx.doi.org/10.4310/ATMP.2019.v23.n2.a3

#### Authors

#### Abstract

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). Supporting a conjectural viewpoint of Juan Maldacena, we show that any such spacetime must have a special geometry similar in various respects to $AdS_2 \times S^2$, and under certain circumstances must be isometric to $AdS_2 \times S^2$.

Published 11 November 2019