I've heard that the size of a black hole is 0 and its density is infinite... :eek:

Well... after thinking about it for a little while, I actually highly doubt that this is true. If that is actually an accepted theory, I would like to point out a few things and ask you guys if I'm missing something.

The gravity is proportional to the density, right? So... if the density is infinite, wouldn't the gravity be also infinite?

Also, the density is defined by the mass over the volume. A black hole doesn't have infinite mass. At the same time, the Volume is really really small. So we can ignore the mass, because the mass is irrelevant compared to the volume (i.e. the Volume is more significant because it is a very small value compared to the mass).

So... since the mass is insignificant, and the volume goes to zero, than the density should be really high. However, if the Volume was zero, than we would have m/0, and the density would be undefined. That would be like an assymptote in the graph. So the density would be going to infinity. But if the density is infinite, than the black hole would be swalling up the entire universe (which we know it doesn't happen).

In other words - there's no singularity in the middle of a black hole. Black holes should have a very small volume that goes to zero, but not an absolute zero.

I believe when we talk about the gravity within a black hole, rather than talking about the perimeter in which the black hole expands we are describing the intensity of the gravity around the black hole. So when they say gravity is infinite, they mean that the strength of the gravity goes on forever, rather than the reaches of the black hole.

Hi truthseeker,
Gravity is porportional to mass, not density.

In the GR model, the black hole singularity has infinite density and zero volume from the point of view of an external frame. Locally, the size and density are not well defined, since the local curvature is infinite.

Yes the gravity would be infinite, but only on an infinitesimal level (the singularity).

No, if the gravity was infinite then what TruthSeeker said would be right. Gravity is not infinite though but increases if more and more matter are 'sucked' into the hole. Remember gravity depends on mass alone. The only infinite thing is the density.

O-k... So we don't really know very well how a black hole is, right...? :D

Anyways... I don't understand the gravity-mass thing. I mean... the density is just how much mass there is in a given volume. So... wouldn't that make gravity proportional to the density? Because they are very closely related, right?

No, because you can get infinite density with anything, the chair you are sitting in, if you smash it down to an infinitely small point of size. You would have created a black hole (that would last a split second) that had infinite density, but certainly not infinite mass nor infinite gravity.

Most black holes you think of have stellar mass or multiples thereof. Even that much mass is nowhere near infinite anything. Disentangle the concept of mass and density. Mass creates gravity, not density. Low density (like a gas) simply puts the “surface” farther from the center of gravity. High density (like a rocky planet) has the surface closer to the center of gravity. At a black hole, the surface and the center are the same place.

Visualize a gas cloud with several dozen stellar masses or more. The eagle nebula. Which generates more gravity, it or several dozen nice compact stars?

If they are of the same mass, it’s a tie. One is just more spread out than the other. A black hole is the opposite. That is, the ultimate in compact.

No, if the gravity was infinite then what TruthSeeker said would be right. Gravity is not infinite though but increases if more and more matter are 'sucked' into the hole. Remember gravity depends on mass alone. The only infinite thing is the density.

I take bake what I said earlier, Gravity isn't INFINITE at the singularity, but the escape velocity is.

I've just talked with my calculus teacher a few minutes ago and he said that the volume can not be 0 and the density can not equal to infinity unless you speculate and/or use some philosophy. He also cited the Heisenberg Uncertainty Principle...

My original question was that the volume in the black hole cannot be 0 because that would make the equation Density=M/V undefined. If the volume approches zero, tough, than the density would approach infinity, but not reach it. What is "infinity" anyways? Is it a defined number?

Now, I would like to propose something. Let us assume that this is right, and the volume approaches 0, while density approaches infinity. Than, what would be the exact value for the volume? If we could somehow find the exact value of the volume, we would also might be able to find the value of density. If we can find those two values, we would find both the smallest and biggest possible value in the universe, and we would than be able to define infinity.

Also, here are a couple of another questions:

Is there dark matter inside a black hole?
Can a black hole be made of just dark matter?

Gravity cannot have infinite reach because that should give it equal pulling power all over the universe.

No, pulling power is stronger close to the gravitational source, and weaker further away. That's not equal!

But even though it gets weaker the further away you go, it never diminishes to zero (according to Newtonian gravity and GR models), meaning it has infinite reach.