Talking to my father tonight, he brought up an interesting concept

[xiphias]

Okay. So, apparently, a black hole does not actually need to be super-dense. It's just, the less dense it is, the bigger its radius has to be in order for it to be a black hole.

A solar-system-sized black hole would only need to be about as dense as air. If you made a big sphere the size of the orbit of Neptune, and filled it with air -- that'd be a black hole.

Here's the weird thought. Um. Not that that previous thing ISN'T a weird thought. But here's a weirder one:

The density of the intergalactic medium is probably something like one hydrogen atom per cubic meter. Not very dense.

But nonetheless, a density.

That means that there exists a radius such that the entire universe is a black hole. And it's calculable.

Which puts an upper bound on the size of the universe. And leaves the possibility that our entire universe is, in fact, on the black hole side of an event horizon.

Comments

[gilmoure.livejournal.com]

I'm not sure how this is supposed to work. I mean, a black hole is a gravity gradient at the point where it's 'too steep' for light to escape, isn't it? How does this correlate with density? I mean, I understand that, the denser something is, the steeper it's gravity field but wouldn't expanding it's radius result in a less steep gravity slope and then you wouldn't have a singularity/Schwartzchild Radius?

[xiphias.livejournal.com]

You DO have a Schwartzchild radius. It's just very, very big.

[brooksmoses]

No, you've got that backwards. His Schwartzchild radius is teeny-tiny, much smaller than he is, and since he's not all within that radius, he's not a black hole.

However, there is an amount of mass which, if packed into a sphere with the same density he has, would be a black hole. It has a radius about the distance of Mars from the sun, IIRC from the article. Which, if you packed it with stuff at that density, is still a startling lot of mass.

[brooksmoses]

You're thinking about it in terms of a fixed amount of stuff, which doesn't quite work, for the reasons you're thinking of. In particular, for any given amount of mass there's a corresponding Schwartzchild Radius, and if you compress the mass densely enough to fit within that radius, it's a black hole, and if it's larger so it doesn't fit within that radius, then it's not.

Instead, though, consider taking a sphere of constant density. If you expand the radius of that sphere, then it's got more stuff in it -- the mass of the sphere increases as the radius cubed.

Now, the trick is because of the interesting fact that the Schwartzchild Radius is proportional to the mass of an object.

So, if you take this sphere, and expand it by adding mass, keeping the density constant, then the gravity slope at the edge keeps getting larger, and eventually it will become a black hole -- no matter how non-dense it is.

An intuitive way to think about it is to imagine that you take a sphere, and pick a point on the surface of it. Now, keep that point fixed, and add stuff on the other side of the sphere to make it a larger sphere. All that stuff you're adding is on one side of that point, so it increases the gravity gradient there. Keep adding stuff, and the gradient gets higher and higher, and eventually it will reach the "too steep" state.

[browngirl.livejournal.com]

That's a great explanation. Thank you.

*reads and contemplates*