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

TL;DR

This paper derives the most general asymptotically $AdS_2 imes S^2$ metrics satisfying the Null Energy Condition, providing explicit examples that differ from the standard product space.

Contribution

It introduces a comprehensive metric ansatz compatible with previous constraints and explores new solutions satisfying physical energy conditions.

Findings

Explicit asymptotically $AdS_2 imes S^2$ metrics found

Examples satisfy Null Energy Condition but differ from standard $AdS_2 imes S^2$

Curvature analysis supports the existence of diverse solutions

Abstract

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 $AdS_2\times S^2$.