2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/33728We 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.2 pages, ws-p9-75x6-50.cls with LaTeX2e. Contribution to the Ninth Marcel Grossmann Meeting (Rome, 2-8 July, 2000). Parallel session GT1General Relativity and Quantum Cosmologytext