  We study the causal dynamics of an embedded null horizon foliated by
marginally outer trapped surfaces (MOTS) for a locally rotationally symmetric
background spacetime subjected to linear perturbations. We introduce a simple
procedure which characterizes the transition of the causal character of the
null horizon. We apply our characterization scheme to non-dissipative
perturbations of the Schwarzschild and spatially homogeneous backgrounds. For
the latter, a linear equation of state was imposed. Assuming a harmonic
decomposition of the linearized field equations, we clarify the variables of a
formal solution to the linearized system that determine how the null horizon
evolves. For both classes of backgrounds, the shear and vorticity 2-vectors are
essential to the characterization, and their roles are made precise. Finally,
we discuss aspects of the relationship between the characterizing conditions.
Various properties related to the self-adjointness of the MOTS stability
operator are extensively discussed.
