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Integrability conditions for vacuum spacetimes with a Killing vector field

Francesc Fayos·Carlos F. Sopuerta
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Abstract

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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Francesc Fayos, Carlos F. Sopuerta. 2000-12-05. Integrability conditions for vacuum spacetimes with a Killing vector field. https://arxiv.org/abs/gr-qc/0012016

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