No black holes after all?

You're not taking into account that as the mass of the black hole increases, the event horizon "moves outward" and overtakes the infalling matter.

Remember, the theory here is that the event horizon never actually happens. Even as the mass increases and move outward, it is limited to expand at the speed of light and subject to time dilation, too, isn't it? Isn't the current theory that even gravity is limited to the speed of light and, if so, isn't it also subject to the time dilation of the mass creating it? What I'm visualizing is like a mathematical curve that approaches 0 but never reaches it, even at infinity. It can't, because each baby-step closer takes longer and longer. As the mass gets closer to the density needed to create a true event horizing, it takes longer and longer to compress that little bit more.

[Geek alert: the event horizon isn't actually a thing and it doesn't actually move. It just represents the distance at which you lose sight of stuff as it goes around the bend in the curved spacetime.]

Yeah, I got that, which is why the whole name "hole" is a bit misleading, in my opinion.

And because the Schwarzschild radius is proportional to the mass of the object (as opposed to the cube root of the mass, as is the case with the Earth), the radius grows much faster than you might think, so that the density of the black hole decreases as the square of the radius as the object grows.

The question is whether the time dilation caused by the mass, as it approaches sufficient density to create an event horizon (and effectively make time stop), ever lets the mass finish compressing to the point where it forms a black hole, at least before the end of time (remember, too, that the velocity of the masses involved also contributes to dilation). Velocity has a time component and as time dilates toward 0, velocity with respect to observer frames of reference outside of the black hole also approach zero. In other words, as the mass density approaches the point where it could create an event horizon, time slows toward 0, thus as the mass compresses more and more, the time it takes to compress a little more increases toward infinity.

Matter outside of the event horizon may be denser than the current black-hole density, so that a new event horizon will form outside of it. In the scenario you painted, with an influx of matter creeping, Achilles-like (from your point of view), towards the event horizon, this will eventually have to happen. The mass of the stuff piling up will bend the space around it. The tortoise will step backwards.

How can even a tortoise take a step before the universe comes to an end when the time dilation component of it's frame of reference approaches zero? Consider that this is all happening within a frame of reference where time is heavily dilated and motion of any sort (be it compression, falling, etc.) slows to a point approaching no advancement in time. Yes, from the frame of reference of the particles in the black hole, things compress and the event horizon expands near the speed of light and it all happens almost instantaneously. But from the outside frame of an outside observer (us), everything going on near the mass slows to near stop such that even a tortoise step takes literally forever.

To put my question a different way, if the event horizon is the point at which time stops for the local frame of reference, how can anything, even gravity, move outward from it? In fact as mass increases toward the point where time stops, can it ever compress to reach a density at which time stops or will it forever be approaching the point at which time stops but never actually reaching it?

"No black holes after all"

She's still around, she just lost a primary is all.

Thats "hose", no black hose can be found...

There are black holes...
They are called givernment programs.. once enacted they never go away and they always just SUCK...