I have understood that merging black holes emit considerable amount of their mass as gravitational waves (up to 5-10%). Based on what I have understood from gravitational waves, the closer black holes are to merging, intensity (both frequency and amplitude) of these waves become stronger.
I am thus assuming much of the total GW output happens during the last "orbit" of the inspiral, and that the origin of these waves is located within "the final orbit", i.e. really close to event horizons of both black holes, my question is essentially, is it possible for such GW to collapse into a black hole themselves (something like a kugelblitz I believe), since there's just a lot of energy in GWs (say a few solar masses) in such small volume of space (say tens of kms cubed)?
I believe this might depend on the size of merging black holes, as both intensity of GWs as well as size of event horizons depend on the mass. I have a gut feeling that smaller black holes might be closer to this limit but maybe both the intensity and event horizon size depend linearly on the mass, and this does not matter at all.