For LTB dust collapse, type II initial perturbations produce type B black hole horizons (with bifurcating trapping horizons), and vice versa, for any fluctuation profile.
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Primordial black hole formation from a type II perturbation in the absence and presence of pressure
For LTB dust collapse, type II initial perturbations produce type B black hole horizons (with bifurcating trapping horizons), and vice versa, for any fluctuation profile.