[General Battuta]

He didn't know what I do.

[Scotty]

Finite and quantifiable. 

Einstein would disagree with you.

Einstein >>>>>>>>>>>>>>>>>>>>>>>>> You

This should be anathema to anyone who actually works with science.  The prominence of one's personality matters exactly zilch to science.

[QuantumDelta]

As for infinities, aren't the only thing we're sure about being 'infinite' is quite specifically singularities, and - those things kinda break general relativity anyway?

Though there's some interesting quantum physics on blackholes.

A Singularity having 0 mass and extreme gravity is something that can't exist in our universe based on our current understanding with accepted theories.

Everything else is supposed to be finite, no matter how mind boggling big it is~

[General Battuta]

Black holes do have mass, and presumably once we have quantum gravity the 'singularity' will be gone.

[Kosh]

Black holes do have mass

It has a lot of mass, but that mass is also hyper hyper hyper dense.

[General Battuta]

Um, yes, it's infinitely dense, thus the singularity.

[Uchuujinsan]

Are you sure? Where does that infinite density come from? Doesn't general relativity halt the collapse when it's (almost) reaching the event horizon?
To tell you the truth, I don't know of any scientific theory that says anything about the structure of the inside of the event horizon.  Not even the general theory of relativity.

[Rian]

Doesn't general relativity halt the collapse when it's (almost) reaching the event horizon?

Not remotely.

The event horizon is an imaginary line at the Schwarzschild radius of the black hole. It marks the point at which even light cannot escape the black hole, but if you were falling into the black hole you wouldn’t be able to tell when you’d crossed it.

The entirety of the black hole’s mass is contained within the Schwarzschild radius. It is impossible to hold a constant radial position beyond the event horizon, because that would require a velocity greater than the speed of light, so the mass collapses inexorably inward to an infinitely small, infinitely dense point (the singularity).

General relativity actually tells us quite a bit about what happens inside the horizon. The only thing it doesn’t tell us is what happens at the actual point of the singularity.

[Uchuujinsan]

The event horizon is an imaginary line at the Schwarzschild radius of the black hole. It marks the point at which even light cannot escape the black hole, but if you were falling into the black hole you wouldn’t be able to tell when you’d crossed it.

Well, as the event horizon marks the point where time dilation reaches infinity, for an OUTSIDE (meaning: us) observer, it takes an infinite amount of time, meaning it will never cross the event horizon from our POV.

It is impossible to hold a constant radial position beyond the event horizon, because that would require a velocity greater than the speed of light

Ehm.. no.
The Schwarschild radius is defined via the escape velocity, not via a velocity to hold a constant position.

[Rian]

Ah, reference frames. Yes, the external observer would see infalling objects appear to freeze at the event horizon, at least until they’re redshifted out of view. That doesn’t mean they actually stay there.

Within the event horizon the escape velocity is greater than the speed of light. That means that even light is forced to fall toward the center of the black hole.

Is that clearer?

[Uchuujinsan]

Given that our outside universe did only exist for a finite time, and our observation exists only for a finite time, it does mean, yes, for us the collapse stops.

That means that even light is forced to fall toward the center of the black hole.

That conclusion simply doesn't follow. You are assuming the mass is concentrated in the center. How do you know that? What theory does say that?

I don't study physics, so I honestly expect that you could show me such a theory.
But just to say this for everyone: I have used lot of my free time to learn about modern (and not so modern) physical theories and hypotheses, so you don't have to try to teach me the basics. Don't tell me the pop science, tell me the real one :/

[edit]
Added an emphasis.

[General Battuta]

The hole actually only has mass, charge, and angular momentum, so technically it doesn't have 'infinite density' in that one could divide the mass by the volume defined by the Schwarzchild radius and get a volume. Nonetheless, the singularity is an infinitely dense point.

It is impossible to hold a constant radial position beyond the event horizon, because that would require a velocity greater than the speed of light

Ehm.. no.
The Schwarschild radius is defined via the escape velocity, not via a velocity to hold a constant position.

Ehm, yes. You're wrong, she's right. There are no stable orbits inside the event horizon. In fact there aren't any within 3 Schwarzschild radii of the center.

That conclusion simply doesn't follow. You are assuming the mass is concentrated in the center. How do you know that? What theory does say that?

No, that assumption is not being made.

You can treat the inside of the event horizon as a homogeneous distribution of mass or as a point source. It doesn't matter. Light must fall towards the center.

[Rian]

This is a good place to start. If you want to make a formal study of it, Taylor and Wheeler’s Exploring Black Holes is a text that does not require graduate-level study to understand, though it assumes an undergraduate-level understanding of special relativity and calculus.

The Schwarzschild metric is invalid beyond the event horizon, but the coordinates described in the article I linked have no discontinuity at the Schwarzschild radius and describe the interior of the black hole. Using these coordinates it’s fairly simple to show that any mass that crosses the event horizon will be inexorably pulled inward, like a boat going over a waterfall. Given sufficient time all the black hole‘s mass will indeed be concentrated at the center simply because there’s nowhere else for it to go.

[Uchuujinsan]

so technically it doesn't have 'infinite density' in that one could divide the mass by the volume defined by the Schwarzchild radius and get a volume.

And what density does it have non-"technically"?
The original claim was "Um, yes, it's infinitely dense", where does that claim come from?

Ehm, yes. You're wrong, she's right. There are no stable orbits inside the event horizon.

Says who? Results from what theory?
I don't want to calculate the minimum required orbital velocity myself, but after checking the orbital calculator
There seems to be a constant factor:
"escape velocity" x 0,7 = "orbital velocity"
So, light could indeed reach the required speed to maintain a stable orbit.
Of course this (probably wrongly) assumes classical physics

You can treat the inside of the event horizon as a homogeneous distribution of mass or as a point source. It doesn't matter. Light must fall towards the center.

Why?

@Rian
Thx for the book name, that sounds interesting. (Though it might be a little hard to read it in english :/ )

For the coordinate system... yes, it will be pulled inward, but not within finite time by an outside observer, while it is already a black hole according to an outside observer (that's something I didn't explicitly state before, probably a mistake).
So, for an outside observer, something can (and will) have a finite mass distributed in a non zero space, while still counting as a black hole, and to get back to the original statement:

Um, yes, it's infinitely dense, thus the singularity.

It's not infinitely dense.

[General Battuta]

Again, the singularity is indeed infinitely dense because it has no volume.

That's the whole point: it's a singularity.

Says who? Results from what theory?

General relativity.

Your argument is predicated on the fact that you don't know relativity and can't perform the necessary math. For instance:

So, light could indeed reach the required speed to maintain a stable orbit.

Light always travels at the same speed, in all reference frames.

It's not infinitely dense.

The singularity has no volume and thus by definition is infinitely dense. THIS IS WHY IT IS A SINGULARITY.

The black hole has mass, charge, and angular momentum, but no other properties (the no-hair theorem.) The singularity itself has infinite density.

[Rian]

Of course this (probably wrongly) assumes classical physics

You can’t assume classical physics inside or even near a black hole.

General relativity states that there are no stable orbits inside a black hole. It also predicts that the black hole’s matter will be concentrated in a single central singularity. While this cannot be conclusively proved without actually entering the black hole, the predictions of general relativity are unambiguous here. This has already been explained two or three times in various terms.

For the coordinate system... yes, it will be pulled inward, but not within finite time by an outside observer,

Because an outside observer cannot see inside the event horizon, the perspective of an outside observer is irrelevant. If you want to know what happens inside the black hole, you go to a coordinate system that actually works inside the black hole. One example is described in the article I linked.

[General Battuta]

We can argue about this all day but until you do the math you won't fully understand it. I highly suggest learning general relativity and working out a black hole example.

The take-home point for now is that a black hole contains a singularity, which is a point where theory breaks down: an infinitely dense (but finitely massive) entity.

Also, there are no stable orbits within the event horizon; once inside it is impossible to avoid intersecting the singularity.

[Uchuujinsan]

To finish this:
It's been news to me that effects inside of black holes (=inside of the event horizon) are considered to be describable accuratly by general relativity, as it starts to conflict with quantum dynamics. As such, literature I read presented those results only as a hypothesis, never as an applicable theory.

[General Battuta]

You did not completely misunderstand what you read.

General relativity is required to describe the properties of extremely massive bodies. Black holes are thus largely described by GR, which can make many useful statements about their properties.

Quantum mechanics is required to describe the properties of extremely small bodies. Singularities are very small.

The reason the singularity is a singularity is because QM and GR are incompatible, and attempting to use them together results in a divide by zero error.

If we had quantum gravity, there wouldn't be a singularity. But this doesn't change the fact that black holes are primarily described using the mathematical tools of general relativity, which make a number of predictions about the interior of the event horizon. The math breaks down at the singularity itself.

[Thaeris]

And the final answer?

Celestial bodies such as black holes are studied as they are not fully understood. No one here has all of the necessary data to close this argument.