  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.
