Classical and Quantum Gravity· 2026Q1
Bartnik's splitting conjecture with the null energy condition
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- Q1SCImago
- 2026year
Short summary
Replacing the strong energy condition with the null energy condition invalidates Bartnik's splitting conjecture in dimensions 3+, showing all globally hyperbolic spatially compact conformal classes contain future complete metrics satisfying the null energy condition.
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Key points
- Bartnik's splitting conjecture is shown to be false when the strong energy condition is replaced by the null energy condition.
- In dimensions 3 and above, all globally hyperbolic spatially compact conformal classes contain future complete metrics satisfying the null energy condition.
- The flatzoomer method is the primary tool used to establish this result.
- The conclusion of the conjecture is proven to be wrong under the modified energy condition.
AI-generated from the title and abstract; the full text is not read.
Abstract
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.
The authors' abstract, as published at the source. Classical and Quantum Gravity, 2026 · DOI ↗
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Field: Applied Mathematics
Applied MathematicsMathematics