2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/693Through the geodesic analysis of a static and axially symmetric space time, we present conditions on the state equation of an isotropic perfect fluid $p=ωd$, when it is considered as dark matter in spiral galaxies. The main conclusion is that it can be an exotic fluid ($-1<ω<-1/3$) as it is found for Quintessence at cosmological scale.4 pages, no figures. Requires REVTeX. Misprints corrected and references updatedAstrophysicstext