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

We find the most general metric ansatz compatible with the results of Galloway and Graf \cite{GG} constraining asymptotically $A d S_{2} \times S^{2}$ 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 $A d S_{2} \times S^{2}$ metrics, in the sense of \cite{GG}, and which satisfy the Null Energy Condition but which differ from $A d S_{2} \times S^{2}$ .

Asymptotically $A d S_{2} \times S^{2}$ metrics satisfying the Null Energy Condition

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Asymptotically $A d S_{2} \times S^{2}$ metrics satisfying the Null Energy Condition

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Asymptotically AdS2×S2AdS2​×S2 metrics satisfying the Null Energy Condition

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Asymptotically AdS2×S2AdS2​×S2 metrics satisfying the Null Energy Condition

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Asymptotically $A d S_{2} \times S^{2}$ metrics satisfying the Null Energy Condition

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Asymptotically $A d S_{2} \times S^{2}$ metrics satisfying the Null Energy Condition

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