  We find the most general metric ansatz compatible with the results of
Galloway and Graf \cite{GG} 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 \cite{GG}, and which satisfy the Null Energy Condition but which
differ from $AdS_2\times S^2$.
