Advances in Theoretical and Mathematical Physics

Volume 23 (2019)

Number 2

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

Pages: 403 – 435



Gregory J. Galloway (Department of Mathematics, University of Miami, Coral Gables, Florida, U.S.A.)

Melanie Graf (Faculty of Mathematics, University of Vienna, Austria)


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