# Space shrink near black holes

1. Apr 1, 2004

### Mike2

I wonder, doesn't GR predict that space shrinks near the surface of a heavy mass such as a black hole.

If you had the power to put and remove objects from orbit around a black hole, then wouldn't a black hole be a perfect storage fascility? You could put many large objects in orbit around a black hole, there size would shrink so that you could put a lot of large objects around what you would preceive from a distance to be a relatively small volume. Is this right?

If time also dialates near black holes, would you actually see anything orbiting? Or would it look to us far away as though it was standing still or moving very slowly?

Thanks.

2. Apr 1, 2004

### Hurkyl

Staff Emeritus
Well, you have the slight problem of tidal forces shredding whatever you're trying to store.

3. Apr 1, 2004

### Mike2

Now I'm confused. Are you saying that space stretches out and elongates objects (to the point of shredding) that approach a black hole? I thought space contracted near black holes.

4. Apr 6, 2004

### JJ

Don't take my word as gospel, cause I'm only an amateur of relativity.

Time will slow down quite considerably for the orbiting junk, depending of where it's orbiting. Take earth, for example: time goes 1.000000001 times slower at its surface! Time will only freeze at the event horizon, where time dilation is infinite.

The thing with extremely strong gravitational fields is that they increase very fast the closer you get to the source. Yeah, that's true for all gravitational fields, due to the inverse square law, but this time the difference in pull between your legs and your head is strong enough to pull you apart. See, if your feet are one meter away from a mass and your head two meters, the gravitational force will be four times stronger at your shoes (2^2:1^2). The difference in forces is what pulls your body to shreads or spaghetti.

Another problem I see are the orbital speeds, which are proportional to the intensity of the gravity. I haven't calculated it, but I'm guessing it can reach the speed of light at the event horizon (where photons are in orbit).

Gah, hope that informs you.

5. Apr 6, 2004

### Mike2

Thank you. But what I'd really after is a confirmation that space shrinks near black hole, etc.

6. Apr 7, 2004

### turin

Look into the "Schwarzschild metric." It depends on what you mean by "space" and what you mean by "shrink." You may think that I'm trying to argue semantics, but actually, when you study GR, you find that these notions are not all that well defined. Also, geodesics will diverge in the radial direction (from the pole of a geodesic coordinate system) and converge in the transverse plane (towards the pole) as time goes on. If you want to consider the metric as the most meaningful representation (as I would) of space, then transverse space shrinks and radial space expands near a black hole.

7. Apr 7, 2004

### chroot

Staff Emeritus
Yup -- you get squeezed together around the waist and pulled apart head-from-feet. You're spaghettified, as the common expression goes.

- Warren

8. Apr 7, 2004

### Mike2

I'm asking more from the perspective from far enough away. Woundn't it appear from a safe distance that large objects are occupying a smaller amount of space as viewed from all angles at safer distances (assuming they could survive and you could get them out)(also assuming that they don't actually cross the event horizion or collide with some other orbiting object)?

Thanks.

9. Apr 7, 2004

### PRodQuanta

As for the shrinking aspect, here's an analogy. Since a black hole is severe warping of spacetime by a concentrated mass, you could think of a bowling ball and a trampoline. Put the bowling ball in the middle of the trampoline, and observe what happens. Of coarse you know that it will warp, but what happens to the springs? That's right, they expand, to make up for the fabrics shrinking in circumfrence. Now make the trampoline a sphere, and you have the reason why it shrinks.