The gravitational instability of kinks is scrutinized in the context of information entropy, including the black hole formation near the scalar field critical collapse. The differential configurational entropy (DCE) is computed and examined for globally perturbed static kinks and the far-from-equilibrium kink solutions as well. In the case of the first kink, the DCE determines a critical value of the perturbation parameter regulating points of bifurcation that characterize a phase transition, whose supercritical range leads to collapse and subsequent black hole formation. For the far-from-equilibrium kink solutions, the DCE supports black hole formation.

10 pages, 4 figures, published version