3-d model for space and black holes

[ecl1pse]

Today I was conversing online in a gaming community and we began talking about relativity. Eventually we started talking about the "fabric of space and time" and how the common model to represent this idea was the old 'ball on a trampoline' idea; a 2-d model.
To get straight to the point, we started thinking about making a 3-d model to represent 3-d black holes in 3-d space and I came up with an idea:

Let's take a sponge, or spongy material, and carve it into a sphere. Let's make the sphere have a radius of 5 inches. Now carve out 2-5 cylinders from the sphere (scattered around the sphere, at opposite ends of each other), approximately 3 inches long. Attach one inch long springs of different resistances to the inside of the cylindrical holes, and have magnets attached to the springs that are about 2 inches long. Also note the alignment of the magnets. For this example, let's have the north polarity facing outwards. The magnets should be able to slide in the cylindrical holes, but not move completely out because the springs are attached to the magnets and the sphere itself. Now let's have a flexible membrane cover that sphere, making sure it is attached or glued at points that it comes into contact with the magnets. Afterwards, let's take a spherical magnetic shell with a radius of 7 inches, its inner side having a north polarity. Encase the first spongy sphere inside the magnetic shell, and have beams supporting the inner sphere to rest in the center of the outer shell, allowing it to be centered and suspended. Since the outside shell is a magnet, and it is not going to move, the polarity (north) is going to oppose the polarity of the magnets inside the inner sphere (also north), causing them to be pushed into the spongy sphere. And since the membrane surrounding the spongy sphere is attached to the magnets in the spongy sphere, it will stretch and form a concavity (due to the spongy material) with the magnets at those points. The varying resistances in the springs will result in varying depths of the concavities. In this 3-d model, the concavities represent black holes in space.

Any input from anyone or extensions of ideas for this would be greatly appreciated.
I simply hate the 'fabric' model because of its improper visuals (although conceptually correct) and I wanted to be able to provide a more visually accurate model for people to better understand 3-d space as opposed to 2-d.

-Mike

 

[Frame Dragger]

You want to go through all of that trouble instead of the usual mathematical diagrams used... why?

Anyway, if you want to model space-time or BHs, I'd use a computer, and leave the sponges and magnets in the kitchen. If you know how to think about them, existing simple diagrams that model the relevant forces and conditions at/in a BH are pretty intuitive and takes the inseperable aspect of spacetime into account.

 

[ecl1pse]

moreso for a physical demo

 

[Frame Dragger]

moreso for a physical demo

If that's really your goal, just buy a black bowling ball, drill a hole through it, skewer it (polar jets) so that you can spin it by hand or crank. Use modeling cement to stick some long threads (or yarn) every inch or so around the circumference of the ball perpendicular to the "polar jets". Repeat this moving towards the "poles" in 1 inch increments. You should have a big fuzzy bowling ball on a stick now, that spins. Spin it.

You're now demonstrating the exotic regions of space-time that could ever be observed of a BH; the Ergoregion where Rotational Frame Dragging occurs, and the pitch-blacl event horizon.

Now, if you wanted to be REEEAAALLLY good, buy undyed yarn for the model. Gradually dye it darker towards the bowling-ball end, redder and redder, and then black at the EH.

That, or go for a "sliced" Matryoshka Doll approach that models both regions. That would take some experience making nested models, and more money.

EDIT: Obviously, the length of the string has to maintain a proportional relationship with the circumference of the ball; the strands should be shorts and shorter and vanish at the poles.

 

[A.T.]

Eventually we started talking about the "fabric of space and time" and how the common model to represent this idea was the old 'ball on a trampoline' idea; a 2-d model.

I simply hate the 'fabric' model because of its improper visuals (although conceptually correct)

The 'ball on a trampoline' in not a conceptually correct analogy to gravity in General Relativity. It lacks the time dimenson. This are conceptually more correct analogies:
http://www.physics.ucla.edu/demoweb..._and_general_relativity/curved_spacetime.html
http://www.relativitet.se/spacetime1.html
http://www.adamtoons.de/physics/gravitation.swf
They also show just a 2D space-time, but that is enough to explain the concept.

and I wanted to be able to provide a more visually accurate model for people to better understand 3-d space as opposed to 2-d.

This are contradicting goals. Adding dimensions will make it more accurate but not easier to understand. To be accurate you would have to show a 4D-space-time that is curved. I have no idea how this would look like, but I doubt people would understand it.

 

[pervect]

The most useful embedding I've run across is to embed the 2 dimensional r-t plane of a black hole into a 3-d Lorentzian geometry.

Or to put it more simply, it describes how you can draw SR space-time diagrams on a curved 2-d surface - said 2-d surface being the surface of a 3d object - to get the right answers and correctly represent the geometry of space-time near a massive obejct.

Handy if the person in question understands special relativity, unfortunately there are a large number of people who don't. And saying "you need to understand SR before you can understand GR" is probably true, but not helpful to the curious.

The paper in question is due to Marolf, "Space time embedding diagrams for black holes", unfortunately it's a more difficult read to follow than is really necessary (IMO).