2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35202We study the exterior vacuum problem for first and second order stationary and axially symmetric perturbations of static bodies. The boundary conditions and their compatibility for the existence of an asymptotically flat exterior solution are discussed.LaTeX, 6 pages, uses ere04.cls style, to appear in the proceedings of the Spanish Relativity Meeting ERE'04General Relativity and Quantum CosmologySecond order perturbations of rotating bodies in equilibrium; the exterior vacuum problemtext