Pictorial representation of small-angle interpretation. Formally our request for a small perturbation η ≪ r_s should induce a small-angles interpretation of our results. Nevertheless, we see graphically the reason why we should expect our approximation to hold even if η is not small. As evident in this figure, around the point A, we see the orthogonal direction to the equilibrium surface (dotted yellow) and to the perturbed surface (dotted orange) remains approximatively collinear. In contrast, for larger angles (see point B in figure) the approximation is not as good (and the functions F₁, F₂ present a divergence, see Appendix A). We recover fully the validity of our approximation to the orthogonal case . Note how this divergence can be cured with higher order expansions in η.