2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/207069The conditions for the existence of Killing-Yano tensors, which are closely related to the appearance of non-generic world-line SUSY, are presented for static axisymmetric spacetimes. Imposing the vacuum Einstein equation, the set of solutions admitting Killing-Yano tensors is considered. In particular, it is shown that static, axisymmetric and asymptotically flat vacuum solutions admitting Killing-Yano tensors are only the Schwarzschild solution.10 pages (RevTeX), TIT/HEP-253/COSMO-44General Relativity and Quantum Cosmologytext