No Dynamics in the Extremal Kerr Throat

Details No Dynamics in the Extremal Kerr Throat No Dynamics in the Extremal Kerr Throat

2009-06-12

arxiv.org/abs/0906.2376v3

JHEP 0909:044,2009

Physics

High Energy Physics

High Energy Physics - Theory

42 pages, 3 figures. v3: minor clarifications and corrections

Scientific paper

10.1088/1126-6708/2009/09/044

Motivated by the Kerr/CFT conjecture, we explore solutions of vacuum general relativity whose asymptotic behavior agrees with that of the extremal Kerr throat, sometimes called the Near-Horizon Extreme Kerr (NHEK) geometry. We argue that all such solutions are diffeomorphic to the NHEK geometry itself. The logic proceeds in two steps. We first argue that certain charges must vanish at all times for any solution with NHEK asymptotics. We then analyze these charges in detail for linearized solutions. Though one can choose the relevant charges to vanish at any initial time, these charges are not conserved. As a result, requiring the charges to vanish at all times is a much stronger condition. We argue that all solutions satisfying this condition are diffeomorphic to the NHEK metric.

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