  We discuss the problem of the X-ray absorption in a system of interacting
fermions and, in particular, those features in the X-ray spectra that can be
used to discriminate between conventional Fermi-liquids and novel "strange
metals". Focusing on the case of purely forward scattering off the core-hole
potential, we account for the relevant interactions in the conduction band by
means of the bosonization technique. We find that the X-ray Fermi edge
singularities can still be present, although modified, even if the density of
states vanishes at the Fermi energy, and that, in general, the relationship
between the two appears to be quite subtle.
