Integrability conditions for vacuum spacetimes with a Killing vector field

Details Integrability conditions for vacuum spacetimes with a Killing vector field Integrability conditions for vacuum spacetimes with a Killing vector field

2000-12-05

arxiv.org/abs/gr-qc/0012016v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

2 pages, ws-p9-75x6-50.cls with LaTeX2e. Contribution to the Ninth Marcel Grossmann Meeting (Rome, 2-8 July, 2000). Parallel s

Scientific paper

We present a new approach to the study of vacuum spacetimes with a Killing symmetry. The central quantity in this approach is the exterior derivative of the Killing vector field, which is a test electromagnetic field. Considering the algebraic structure of this quantity we get a new view of the integrability conditions, which provides a natural way of studying the connections between the algebraic structure of the spacetime and properties of the Killing symmetry.

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