Bartnik's splitting conjecture with the null energy condition

Abstract Bartnik conjecture is one of the prime open conjectures in mathematical relativity. There are many approaches to this conjecture that use (Lorentzian) conformal geometry. In this article, we show that if we replace the strong energy condition in Bartnik's splitting conjecture with the null energy condition, then in any dimension greater or equal to $3$ the conclusion of the conjecture would be wrong, more precisely: On a manifold of dimension at least $ 3$, {\em every} globally hyperbolic spatially compact conformal class contains future complete metrics satisfying the null energy condition. In the spatially noncompact case, the same is true in the future of any Cauchy surface. The main tool is the flatzoomer method.