A 10 billion light year wide Black Hole? Huh?

[Alex_Dubinsky]

@Frylock

What if the entire visible universe were to collapse into a black hole? How big would that be?

The visible universe has in the magnitude of 100 billion galaxies. Since radius is proportional to mass, let’s see… 100 billion times 0.1 light year is 10 billion light years.

Holy crap! It WOULD be as big as our universe. Although, it’s sort of hard to say how big our universe is, since although we know how old the universe is, we apparently don’t exactly know how fast it’s been expanding. Wikipedia claims 100 billion light years or more.

Then again… did the person with the “0.1 light year for galaxy” figure take into account dark matter? What about dark energy? No? I didn’t think so. So knock the universal black hole up into the 100’s of billions or so.

[Chronos]

Quoth bup:

I think you run into a speed-of-light speed limit problem there. Before the instant they touch, you have two separate black holes, each with its own gravity field. If they are roughly the same size, it’s easy to see that there is even a point between them where the net effect of gravity is zero, and the other points on the plane that bisects them (you know what I mean) that have net effects of gravity nothing close to inescapable.

Then at the instant they touch, every point inside the Schwarzchild radius implied by their combined mass is doomed? There has to be some time before that happens.

The key to realize here is that an event horizon is a global phenomenon, not a local one. Theoretically at least, you need to be able to observe the entire Universe to be able to tell where an event horizon is (though in practice, you can usually make a pretty good guess, based on local conditions). Since the location of an event horizon can’t be observed locally, the formation of an event horizon can’t transmit information.

Oh, and Chronos, you maybe never saw this post, but I am still interested in what specific sort of mental things you pondered to help you visualize a fourth spatial dimension.

No, just not much to say on the topic. I just kept trying to visualize things like four mutually-perpendicular lines (or hypercubes, or hyperspheres, or whatever). Usually, I screwed up and ended up squeezing all four lines into three dimensions, but eventually I got the the point where I wasn’t.

Quoth ZenBeam:

The Schwartzschild is an isolated solution, found assuming negligible mass near the horizon (or at least assuming a spherically symmetric mass distribution). I would expect that the BBH horizon would bulge out on the side near the SBH, so that the two horizons would merge when the two singularities were farther apart than the sum of their Schwartzschild radii.

I was oversimplifying rather a bit there. Yes, there are tidal bulges before they actually merge. The end result is still that they merge the moment the horizons touch.

As for the whole Universe-as-black-hole thing: Without considering dark energy, the condition for the entire Universe to be a black hole is exactly the same as the condition for the Universe to be closed. The Big Crunch singularity at the end of the universe is the singularity at the center of the hole. With dark energy, the situation’s a bit more complicated, but suffice to say that the cosmic black hole is no longer considered a possibility. But the Universe is still not all that tremendously far from the conditions under which it would be a black hole (within an order of magnitude or so), so it’s not surprising that the possibility would still show up on a back-of-the-envelope estimate.

[elucidator]

Math nerds. Gimmee yer lunch money!