  Five-dimensional domain walls in gauged $SU(5)$ generate a position-dependent
symmetry breaking pattern along the additional dimension. We analize the
perturbative stability and the 4D spectrum of these walls in the
self-gravitating case, in terms of diffeomorphism- and Lie algebra
gauge-invariant field fluctuations. We show that tachyonic modes are absent,
ensuring perturbative stability. As expected, gravitational tensor and vector
fluctuations behave like its counterparts in the standard $Z_2$ domain walls.
All the Lie algebra valued fluctuations exhibit towers of 4D massive modes
which propagate in the bulk, with a continuous spectrum starting from zero. All
the would-be 4D Nambu-Goldstone fields, which are gravitationally trapped in
the case of a global symmetry, are non-trivially absent. However we find no
localizable 4D gauge bosons, either massless or massive. Instead,
quasi-localizable discrete 4D massive modes for the gauge field fluctuations
are found, along the spontaneously broken directions.
