  Null shells are a useful geometric construction to study the propagation of
infinitesimally thin concentrations of massless particles or impulsive waves.
After recalling the necessary and sufficient conditions obtained in [28] that
allow for the matching of two spacetimes with null embedded hypersurfaces as
boundaries, we will address the problem of matching across Killing horizons of
zero order in the case when the symmetry generators are to be identified. The
results are substantially different depending on whether the boundaries are
non-degenerate or degenerate, and contain or not fixed points (in particular,
in the former case the shells have zero pressure but non-vanishing energy
density and energy flux in general). We will present the explicit form of the
so-called step function in each situation. We will then concentrate on the case
of actual Killing horizons admitting a bifurcation surface, where a complete
description of the shell and its energy-momentum tensor can be obtained. We
will conclude particularizing to the matching of two spacetimes with spherical,
plane or hyperbolic symmetry without imposing this symmetry on the shell
itself.
