# Q: Space expansion and black holes

1. Jan 15, 2009

### grkuntzmd

It is my understanding that with the passing of time, space actually expands in size. In about 14G years, space will be twice its current size.

What will this do to black holes (BH)? If a BH is in intergalactic space and has nothing to consume, if space actually expands, the density of the BH should become 1/2. What happens to the event horizon in this case? Would this cause the BH to eventually disappear, similar to Hawking radiation?

2. Jan 15, 2009

### marcus

Saying "space expands" is an excellent descriptive metaphor. Have a look at the sticky thread about the balloon model.

It is a 2D analog of what happens in 3D.

But you understand I'm sure that verbal descriptions---metaphors---and simple physical analogies are never quite right. Can't push them too far.

"Space expands" should not suggest to you that space is a material (like the rubber of the balloon) or that it expands uniformly. Basically it is just a shorthand non-technical way of referring to something more long-winded.

Distances within our solar system are not increasing as part of this process. Dimensions of black holes and stars are not increasing. Distances within our galaxy are not increasing.
Distances within gravitationally bound clusters of galaxies are not.

The Hubble law is about much larger distances, between objects which are not physically bound to each other. Not orbiting each other. Not in direct contact.
There are millions of galaxies which are not bound in any way to our Milkyway galaxy. The distances that are increasing by Hubble law are to those objects. And they increase with remarkable uniformity. by about 1/140 of a percent every million years.

The percentage rate of increase has been much more rapid in the past.

You can make a rough estimate of how many million years it would take to double, starting now, using logarithms or a compound interest table.
1/140 percent is 1/14000
You have to solve this equation for N (the number of million years)
(1 + 1/14000)N = 2

N = log 2/log (1 + 1/14000)

When I put log 2/log (1 + 1/14000) into the google window and press return, I get 9700. So I think a rough estimate of doubling time is 9700 million years, or 9.7 billion.

However the percentage rate is slowly declining so it might be a bit more realistic to say log 2/log (1 + 1/16000) and when I put that in google I get
11 billion years. So I think your figure of 14G years is right order of magnitude though perhaps a bit on the high side. I'm just doing rough estimates, maybe someone else would like to offer an exact figure.

Note that as we all know the expansion is accelerating but it is also true, as I say, that the percentage rate of distance increase is declining. That is another case where words are being used to describe a mathematical reality. The math meaning of "expansion accelerating" does not mean percentage rate increasing. It means the scalefactor a(t) is increasing at an increasing rate---the second derivative with respect to time. All it takes is first year college calculus, to clarify much of this stuff but people keep on expecting to be told in words and words keep on breeding confusion. Your name suggests you are an MD physician, so maybe you experience this same thing happening in your field.

Last edited: Jan 15, 2009
3. Jan 16, 2009

### Chalnoth

The way that I like to describe it is this:

The expansion of space is driven by gravity. It is an approximation that comes along because on the largest of scales, our universe is uniform. That approximation breaks down when you get to denser regions of the universe, where things are in orbit around one another due to their gravity.

So the same exact force that says that the universe as a whole is expanding also says that the local galaxies, galaxy clusters, stars, black holes, and planets are not.