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Annales Henri Poincaré

, Volume 20, Issue 7, pp 2271–2293 | Cite as

On the Local Extension of Killing Vector Fields in Electrovacuum Spacetimes

  • Elena GiorgiEmail author
Article
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Abstract

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 in Yu (Ann Henri Poincaré 11(1–2):1–21, 2010). 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 in Ionescu and Klainerman (J Am Math Soc 26(2):563–593, 2013) 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 in [5] to the electrovacuum case.

Notes

Acknowledgements

The author would like to thank Sergiu Klainerman and Mu-Tao Wang for suggesting the problem and for valuable discussions.

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA

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