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Bonnet-Myers rigidity theorem for globally hyperbolic Lorentzian length spaces
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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 $L=\frac{\pi}{\sqrt{|K|}}$: It states that the space necessarily is a warped product with warping function $\cos:(-\frac{\pi}{2},\frac{\pi}{2})\to\mathbb{R}_+$. From this, one also sees that a globally hyperbolic spacetime with curvature bounded above by $K<0$ and an open distance realizer of length $L=\frac{\pi}{\sqrt{|K|}}$ is a warped product with warping function $\cos$.
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Cited by 1 Pith paper
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New perspectives on the d'Alembertian from general relativity. An invitation
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