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We find the most general metric ansatz compatible with the results ofGalloway and Graf \cite{GG} constraining asymptotically $AdS_2\times S^2$space-times (and a differentiability assumption), and then study its curvaturesubject to a variety of geometrical and physical restrictions. In particular wefind explicit examples which are asymptotically $AdS_2\times S^2$ metrics, inthe sense of \cite{GG}, and which satisfy the Null Energy Condition but whichdiffer from $AdS_2\times S^2$.

Asymptotically $AdS_2\times S^2$ metrics satisfying the Null Energy Condition