On completeness of orbits of Killing vector fields

Details On completeness of orbits of Killing vector fields On completeness of orbits of Killing vector fields

1993-04-21

arxiv.org/abs/gr-qc/9304029v1

Class.Quant.Grav.10:2091-2102,1993

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

16 pages, Latex, preprint NSF-ITP-93-44

Scientific paper

10.1088/0264-9381/10/10/016

A Theorem is proved which reduces the problem of completeness of orbits of Killing vector fields in maximal globally hyperbolic, say vacuum, space--times to some properties of the orbits near the Cauchy surface. In particular it is shown that all Killing orbits are complete in maximal developements of asymptotically flat Cauchy data, or of Cauchy data prescribed on a compact manifold. This result gives a significant strengthening of the uniqueness theorems for black holes.

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