Static Vacuum Spacetimes with $Λ<0$ as Attractors of the Ricci-Harmonic Flow
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866918466375647232 |
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| author | Jouttijärvi, Rasmus Kroencke, Klaus Yudowitz, Louis |
| author_facet | Jouttijärvi, Rasmus Kroencke, Klaus Yudowitz, Louis |
| contents | We prove dynamical stability and instability theorems for asymptotically hyperbolic static solutions of Einstein's equation with $Λ<0$, viewed as self-similar solutions of the Ricci-harmonic flow. More precisely, we show that static metrics are dynamically stable if and only if a positive mass type theorem holds for nearby metrics. Our key tool is a new variant of the expander entropy for the Ricci-harmonic flow. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_22585 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Static Vacuum Spacetimes with $Λ<0$ as Attractors of the Ricci-Harmonic Flow Jouttijärvi, Rasmus Kroencke, Klaus Yudowitz, Louis Differential Geometry Analysis of PDEs We prove dynamical stability and instability theorems for asymptotically hyperbolic static solutions of Einstein's equation with $Λ<0$, viewed as self-similar solutions of the Ricci-harmonic flow. More precisely, we show that static metrics are dynamically stable if and only if a positive mass type theorem holds for nearby metrics. Our key tool is a new variant of the expander entropy for the Ricci-harmonic flow. |
| title | Static Vacuum Spacetimes with $Λ<0$ as Attractors of the Ricci-Harmonic Flow |
| topic | Differential Geometry Analysis of PDEs |
| url | https://arxiv.org/abs/2604.22585 |