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arXiv · 2401.17017

Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces

Tobias Beran
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Abstract

We prove a synthetic Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces with global curvature bounded below by $K<0$ and an open distance realizer of length $L=\fracπ{\sqrt{|K|}}$: It states that the space necessarily is a warped product with warping function $\cos:(-\fracπ{2},\fracπ{2})\to\mathbb{R}_+$. From this, one also sees that a globally hyperbolic spacetime with curvature bounded above by $K<0$ and an open distance realizer of length $L=\fracπ{\sqrt{|K|}}$ is a warped product with warping function $\cos$.

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Tobias Beran. 2024-12-02. Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces. https://arxiv.org/abs/2401.17017

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