Even a very small blackhole would catch all neutrinos that pass it, right? So maybe we could use them as neutrino detectors and/or sails :) Hm, can we detect

Even a very small blackhole would catch all neutrinos that pass it, right? So maybe we could use them as neutrino detectors and/or sails :) Hm, can we detect big black holes that way - looking at their neutrino shadow?