Advances in Theoretical and Mathematical Physics
Volume 23 (2019)
Rigidity of asymptotically $AdS_2 \times S^2$ spacetimes
Pages: 403 – 435
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