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A Bonnet–Myers rigidity theorem for globally hyperbolic Lorentzian length spaces
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics , First View
- Published online by Cambridge University Press:
- 13 January 2025, pp. 1-42
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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.
