On the Local Extension of Killing Vector Fields in Electrovacuum Spacetimes
| Autor: | Elena Giorgi |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Mathematics - Differential Geometry
Nuclear and High Energy Physics Spacetime Horizon Null (mathematics) Mathematics::Analysis of PDEs FOS: Physical sciences Statistical and Nonlinear Physics General Relativity and Quantum Cosmology (gr-qc) Extension (predicate logic) General Relativity and Quantum Cosmology symbols.namesake Killing vector field Differential Geometry (math.DG) Poincaré conjecture FOS: Mathematics symbols Vector field Mathematical Physics Bifurcation Mathematics Mathematical physics |
| Zdroj: | Annales Henri Poincaré. 20:2271-2293 |
| ISSN: | 1424-0661 1424-0637 |
| DOI: | 10.1007/s00023-019-00811-5 |
| Popis: | We revisit the problem of extension of a Killing vector field in a spacetime which is solution to the Einstein-Maxwell equation. This extension has been proved to be unique in the case of a Killing vector field which is normal to a bifurcate horizon by Yu. Here we generalize the extension of the vector field to a strong null convex domain in an electrovacuum spacetime, inspired by the same technique used by Ionescu-Klainerman in the setting of Ricci flat manifolds. We also prove a result concerning non-extendibility: we show that one can find local, stationary electrovacuum extension of a Kerr-Newman solution in a full neighborhood of a point of the horizon (that is not on the bifurcation sphere) which admits no extension of the Hawking vector field. This generalizes the construction by Ionescu-Klainerman to the electrovacuum case. 20 pages. Version accepted for publication in Ann. Henri Poincar\'e. arXiv admin note: text overlap with arXiv:1108.3575 by other authors |
| Databáze: | OpenAIRE |
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