  We present a dynamical theory of the Auger decay in one-dimensional (1D)
metals described by the Tomonaga-Luttinger model. An analytic expression of the
Auger current is derived in the framework of the 1-step approach, where the
finite lifetime of the initial core-hole and the core-valence interaction are
taken into account. This allows to capture typical dynamical features like the
shake-down effect, in which the Auger spectrum shows a non-vanishing weight
above the 2-step high-energy threshold. The obtained results give also a hint
to understand the sizable suppression of Auger spectral weight closed to the
Fermi energy recently observed in carbon nanotubes with respect to graphite.
