# Paul Tod: Asymptotically $AdS_2\times S^2$ metrics satisfying the Null Energy Condition

**Time: **
Tue 2019-09-17 11.00 - 12.00

**Lecturer: **
Paul Tod, University of Oxford

**Location: ** Seminar Hall Kuskvillan, Institut Mittag-Leffler

### Abstract

We find the most general metric ansatz compatible with the results of Galloway and Graf constraining asymptotically \(AdS_2\times S^2\) space-times (and a differentiability assumption), and then study its curvature subject to a variety of geometrical and physical restrictions. In particular we find explicit examples which are asymptotically \(AdS_2\times S^2\) metrics, in the sense of Galloway and Graf, and which satisfy the Null Energy Condition but which differ from \(AdS_2\times S^2\).