I just read an article on black holes and it explained that they have a point of “infinite density”. Now, I have a hard enough time wrapping my brain around the idea of “infinity”, but this one really threw me. How can something be infinitely dense? Does this infinitely dense point have any volume? I would think that if it was infinitely dense, it wouldn’t take up any space. So what’s the deal, and could I possibly say infinite enough times?
Infinitely thankful,
WIGGUM
Wouldn’t that refer to an asymptotic line whose limit is infinity?
Correct me if I’m wrong, but black holes are not infinitely dense. As long as you have enough mass inside a small enough volume of space, you will have a black hole. Mathematically speaking, if R < 2GM/c^2 where G is the gravitational constant, M is mass, and R is the radius, then you will have a black hole.
The article I read can be found here: http://abcnews.go.com/sections/scitech/DailyNews/spinningholes010501.html and says the following;
I guess it is wrong to say that a black hole is infinitely dense. A black hole includes the area enclosed by the event horizon, so it has volume. If the event horizon were to shrink to a point (presumably through Hawking radiation), the hole would disappear.
What the article probably was trying to describe wasn’t the whole black hole, but the singularity at its center. Some would describe that as infinitely dense, since it does have some mass and does not have any volume.
However, most math mavens would hesitate to use that description. At a singularity, density is not defined. Same as with any division by zero.
In some sense this is all rather a moot point. The reason
that the term “infinitely dense” often is thrown around
when speaking of black holes is that there is nothing
stopping the catastrophic collapse of the object. A black
hole has reached a state where physics knows of nothing
that could resist the gravitational collapse. According
to our currently understood laws of physics (perhaps it
is better to say, “our current models”) since there is
nothing to stop it, the object would in fact be crushed
to a point of zero-volume. The name “singularity” is
a common mathematical term to describe a point where a
function goes ga-ga. If you do the calculations for a black
hole, this zero-volume result is a mathematical sigularity.
This “object” has also come to bear the name “sigularity”
in its own right.
Now, why is this all moot? Because this “singularity” is
unobservable. No information can cross a black hole’s
event horizon. The old (and inaccurate) saying, “Nature
abhors a vacuum,” can be applied to black holes. “Nature
abhors a naked sigularity.” To spare us the trouble of
having to deal with points in space with infinite density,
nature conveniently hides them away behind a event horizon
where they can never be observed.
So, is there a point of infinite density at the center
of a black hole? The real answer is that it is not a
meaningful question. In a very real sense, nothing that
is behind the event horizon exists in our universe except
for its gravitational (and rotational, blah-blah)
influence.
Well, a lot of hyperbole is being tossed about, but it’s really rather simple.
The reason they say it’s “infinite density” is because the singularity of the black hole is predicted to be a point. (It is likely no one will ever verify this first hand, or if they do, that they will be able to tell us about it.) In other words, it has no volume, yet it has rest mass. Since density is mass divided by volume, then you have the rather unique circumstance where the universe is trying to divide by zero.