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arxiv: 2603.20802 · v2 · pith:AYS63I4Xnew · submitted 2026-03-21 · 🌀 gr-qc · math-ph· math.DG· math.MG· math.MP

Curvature bounds, regularity and inextendibility of spacetimes

Tobias Beran , John Harvey , Clemens S\"amann This is my paper
classification 🌀 gr-qc math-phmath.DGmath.MGmath.MP
keywords curvatureboundsinextendibilityspacetimescausalcharacterclassicalcomplementing
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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.

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    Under the strong energy condition, positive lower bounds on asymptotic volume-expansion invariants imply past timelike geodesic incompleteness with explicit time bound; extends to synthetic TCD^e_p(0,N) length spaces.