Curvature bounds, regularity and inextendibility of spacetimes

TL;DR

This paper establishes a new connection between curvature bounds and the causal properties of maximizers in spacetimes, using synthetic curvature to relate low-regularity inextendibility to unbounded curvature, advancing classical methods.

Contribution

It introduces a novel relation between synthetic curvature bounds and the causal structure of maximizers, enhancing understanding of spacetime inextendibility at low regularity.

Findings

Relates curvature bounds to the causal character of maximizers

Links low-regularity inextendibility to unbounded curvature

Strengthens previous results by Grant-Kunzinger-Saemann (2019)

Abstract

We provide a completely new relation between curvature bounds and definiteness of the causal character of maximizers by exploiting the robust notion of synthetic curvature. This enables us to relate low-regularity inextendibility of spacetimes to unboundedness of curvature - which is at present unattainable using classical methods - thereby strengthening and complementing the results of Grant-Kunzinger-Saemann (2019) significantly.