Uh, this is why I tried to study pure maths (it's less physics and more weird differential geometry) I can recommend this paper [0] that talks about simulations that show a black hole just implodes in a weird way and kind of does not stop imploding, due to space-time getting stretched with a speed above that of light, as measured within a frozen moment in time, and summed over some line from inside to outside. A working analogy could be a 2d-spacetime, represented in 3d-space as a soap bubble film. Imagine the traditional visual funnel shape the space time around a black hole is often depicted as, compared to the downwards bump normal stars/planets are depicted. So, now, the thing is that the effect of gravity, e.g. gravitational waves, are bound by the speed of light. They can not escape a black hole. In the soap example the gravity waves would be film thickness waves, e.g. longitudinal waves in the thin soap sheet. Those are bound by the speed of sound in their medium. Imagine a stream of air with significantly higher speed than the sound in the soap, getting blown downwards this funnel. Also imagine the funnnel still having a closed tip made from soap at the start. Thing is, this air will hit the tip, propell it downards, and suck the part close to the center down just by itself, without the center indirectly pulling on it. Due to the supersonic nature, the ripple created from the initial impact of air onto the center will _never_ get out of there, just because the medium the waves travel through, when measured over the distance from where the wave is right now, to where the outside world with neglegible space-time (or soap-film) curvature is, expands faster than the wave travels. This does not mean the wave does not travel at all, just that once the distance you want it to travel increases enough, the propagation medium's expansion results in weird effects.

If someone is willing/able to point me to some research or possibly even wants to use existing skills with the related differential geometry maths, I'd really like that.

Edit: I might add that anything that falls into the black hole will, even in it's own reference frame, _never_ reach the center, and the only reference frame that possibly sees a steady state field curvature in finite local time could be the center of the collapse.

[0]: https://arxiv.org/abs/1402.1524 (Which was published about half a year after I initially and timestamped communicated the idea to a physics teacher who was willing to explain me the differential maths used in Einstein's field equations.)