General matching across Killing horizons of zero order

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