  The perturbation theory plays an important role in studying structure
formation in cosmology and post-Newtonian physics, but not all phenomena can be
described by the linear perturbation theory. Thus, It is necessary to study
exact solutions or higher order perturbations. Specifically, we study black
hole (apparent) horizons and the cosmological event horizon formation in the
perturbation theory. We emphasize that in the perturbative regime of the
gravitational potential these horizons cannot form in the lower order. Studying
the infinite plane metric, we show that to capture the cosmological constant
effect we need at least a second order expansion.
