  We study the stability of vortex-lines in trapped dilute gases subject to
rotation. We solve numerically both the Gross-Pitaevskii and the Bogoliubov
equations for a 3d condensate in spherically and cilyndrically symmetric
stationary traps, from small to very large nonlinearities. In the stationary
case it is found that the vortex states with unit and $m=2$ charge are
energetically unstable. In the rotating trap it is found that this energetic
instability may only be suppressed for the $m=1$ vortex-line, and that the
multicharged vortices are never a local minimum of the energy functional, which
implies that the absolute minimum of the energy is not an eigenstate of the
$L_z$ operator, when the angular speed is above a certain value, $\Omega >
\Omega_2$.
