An example of an asymptotically $AdS_2\times S^2$ metric satisfying NEC but which is not exactly $AdS_2\times S^2$

Paul Tod

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arXiv · 1808.00317

An example of an asymptotically $AdS_2\times S^2$ metric satisfying NEC but which is not exactly $AdS_2\times S^2$

Paul Tod

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Abstract

We give an example of an asymptotically $AdS_2\times S^2$ metric, in the sense of \cite{GG}, which satisfies the Null Energy Condition but is not exactly $AdS_2\times S^2$. It is therefore a counterexample to a conjecture of Maldacena mentioned in \cite{GG}, but it does not satisfy field equations. In an appendix we give an example admitting supercovariantly constant spinors as in \cite{t1}, which is asymptotically $AdS_2\times S^2$ on one side only.

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Paul Tod. 2018-08-01. An example of an asymptotically $AdS_2\times S^2$ metric satisfying NEC but which is not exactly $AdS_2\times S^2$. https://arxiv.org/abs/1808.00317

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