Low regularity approach to Bartnik's conjecture

TL;DR

This paper proves a version of Bartnik's Splitting Conjecture for Lorentzian length spaces, demonstrating that under certain conditions, such spaces split as metric Lorentzian products, advancing understanding of spacetime geometry.

Contribution

It establishes a splitting result for Lorentzian length spaces with non-negative timelike curvature, extending classical conjectures to a broader, low-regularity setting.

Findings

Lorentzian length spaces with non-negative timelike curvature split as products

Causal boundary of such spaces reduces to a single point

Results apply under timelike completeness and global hyperbolicity

Abstract

In this work we establish a version of the Bartnik Splitting Conjecture in the context of Lorentzian length spaces. In precise terms, we show that under an appropriate timelike completeness condition, a globally hyperbolic Lorentzian length space of the form $\Sigma\times \mathbb{R}$ with $\Sigma$ compact splits as a metric Lorentzian product, provided it has non negative timelike curvature bounds. This is achieved by showing that the causal boundary of that Lorentzian length space consists on a single point.