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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
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