Killing Initial Data
R.Beig (Institut f\"ur Theoretische Physik, Universit\"at Wien) Piotr, T. Chrusciel (Departement de Mathematique Faculte des Sciences Tours)

TL;DR
This paper characterizes Killing initial data in terms of lapse and shift on spacelike slices, providing conditions for their Lie algebra structure and applying this to analyze orbit periodicity in asymptotically flat space-times.
Contribution
It offers a necessary and sufficient condition for Killing initial data to form a Lie algebra, linking initial data to space-time symmetries.
Findings
Killing initial data form a Lie algebra under specific conditions
Theorem on periodicity of orbits for certain Killing vectors
Application to asymptotically flat space-times
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
