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arXiv · gr-qc/9604040

Killing Initial Data

R. Beig·Piotr T. Chrusciel
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Abstract

We study space-time Killing vectors in terms of their "lapse and shift" relative to some spacelike slice. We give a necessary and sufficient condition in order for these lapse-shift pairs, which we call Killing initial data (KID'S), to form a Lie algebra under the bracket operation induced by the Lie commutator of vector fields on space-time. This result is applied to obtain a theorem on the periodicity of orbits for a class of Killing vector fields in asymptotically flat space-times.

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R. Beig, Piotr T. Chrusciel. 1996-04-22. Killing Initial Data. https://doi.org/10.1088/0264-9381%2F14%2F1a%2F007

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