On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915417722716160 |
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| author | Metsch, Alec |
| author_facet | Metsch, Alec |
| contents | Extending the recent work of Cannarsa, Cheng and Fathi, we investigate topological properties of the locus ${\cal NU}(M,g)$ of multiple maximizing geodesics on a globally hyperbolic spacetime $(M,g)$, i.e.\ the set of causally related pairs $(x,y)$ for which there exists more than one maximizing geodesic (up to reparametrization) from $x$ to $y$. We will prove that this set is locally contractible. We will also define the notion of a Lorentzian Aubry set ${\cal A}$ and prove that the inclusions ${\cal NU}(M,g)\hookrightarrow \operatorname{Cut}_M\hookrightarrow J^+\backslash {\cal A}$ are homotopy equivalences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22737 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime Metsch, Alec Optimization and Control Mathematical Physics Differential Geometry Extending the recent work of Cannarsa, Cheng and Fathi, we investigate topological properties of the locus ${\cal NU}(M,g)$ of multiple maximizing geodesics on a globally hyperbolic spacetime $(M,g)$, i.e.\ the set of causally related pairs $(x,y)$ for which there exists more than one maximizing geodesic (up to reparametrization) from $x$ to $y$. We will prove that this set is locally contractible. We will also define the notion of a Lorentzian Aubry set ${\cal A}$ and prove that the inclusions ${\cal NU}(M,g)\hookrightarrow \operatorname{Cut}_M\hookrightarrow J^+\backslash {\cal A}$ are homotopy equivalences. |
| title | On the locus of multiple maximizing geodesics on a globally hyperbolic spacetime |
| topic | Optimization and Control Mathematical Physics Differential Geometry |
| url | https://arxiv.org/abs/2507.22737 |