[lostmsu]

Unfortunately can't reply to the original question anymore. But here's another hypothesis I just read elsewhere (RU: https://don-beaver.livejournal.com/212422.html): the matter-energy falling towards "center" inevitably has some non-zero momentum, orthogonal to the direction along r. That means its fall is going to be (sort of) spiral, causing it to produce gravitational waves. The argument here is that the whole mass will be converted into gravitational waves before reaching the central point. Now what happens to those waves is a question still.