How do you visualize black holes in a spacetime fabric?

Question

Many popular science books make reference to black holes. When I picture a black hole, I tend to think of it as a pin-hole in a balloon....I think of this balloon as a universe surrounded by much less dense region. In this way, I think of a black hole like the drain at the bottom of a bathtub, with the matter sucked into it escaping into some other unknown region.

I visualize the black hole this way because I tend of think of the universe like a big balloon (with boundaries). I know this is not correct, but my brain can't imagine a black hole floating freely about in the "balloon's" empty internal volume. Where would the matter escape too?

Question-In-Summary: How should I visualize black holes using some earthly metaphor?

With regard to the first answer below: I saw this documentary a couple of times, and I think it makes the same mistake I do, trying to visualize the universe as some kind of 3 dimentional blob with some galaxies and stars floating about inside of it.

Answer 1

The most common visualization is that of a pool ball on a rubber sheet. The sheet sinks down to a minimum with the ball at the lowest point. This is a good 2d representation. As for 3d, imagine the pool ball sinking into the rubber sheet again, and then add rubber sheets parallel to all of the infinite planes intersecting the ball. The ball also sinks into these. This is a much better picture than the 2d representation, and really shows that the black hole (or any other object) is pulling space in towards itself instead of sinking into space-time like most diagrams show.

We don't really know if the matter goes somewhere else when it enters the black hole, but theoretically it would become part of the singularity, meaning it would pretty much go nowhere.

Answer 2

The black hole solution to the equations of general relativity is actually not all that hard to think about. Like all solutions to the equations of general relativity, it is a curved object in four dimensional space-time, but actually a black hole is spherically symmetric in the space dimensions, and (for the basic formal solution) static in the time dimension. It therefore varies in only one dimension: radius.

At large radii, the solution looks just like ordinary, flat Minkowskian spacetime. As you move inward, however, you find that the area of a sphere surrounding the center is larger than you would expect from a flat geometry, if you measure distance inward from some point far away. That is the basis for the horn-shaped hole that is often used to depict black holes in popularizations, where the depth of the hole is not in any sense real, but is a dimension in a 6-dimensional flat embedding space, and reflects that fact that there is a lot more "distance" to the center than you would expect from measuring a sphere surrounding the center. This state of things continues to get more extreme until you get to the Schwarzschild radius. There, the radial coordinate really blows up and becomes "timelike", meaning that future time now points inwards, toward the singularity at the center. Moving toward the center now becomes as inevitable as moving forward in time, although a person dropping through this radius in a pure vacuum solution would not notice any change. After a finite amount of time, you get crushed at the singularity at the center never to return (or come out anywhere else, for that matter---it's the end of time for you).

Because of this swapping of radius and time at the Schwarzschild radius, it is not possible to compare a black hole to any 3-dimensional object you can visualize. Fundamentally, this comes from the difference between the idea of distance in Euclidean geometry and the idea of distance in Relativity, where there are curves of null (i.e. zero) length connecting many different points.

Answer 3

the visualization with the drain isn't too bad

it just surpresses the third dimension, which must not necessarily be in place to have the complete picture

you may get a better understanding about black holes that they not just consist of an event horizon and thats it.

In fact it has a surface and its just becoming a black hole if the event horizons is somewhere above this surface.
matter falling into it will increase its mass, causing the surface to grow, and the event horizon to be at a greater distance to the surface.
This way black holes can grow to enormous sizes.

The one believed to be at our galaxy center is believed to have the size of our complete solar system.

so theres nothing wrong with your 2D visualization, cause any 3D view on it from a single location in space is like having a 2D picture.

The whole story just gets a little more tricky if you consider what happens to time if objects fall into it. The time passing for an observer, and the time for somone falling into it.

Answer 4

ummm yeah!!!! Seriously though I know that we are to think of this flat plane in the universe but I'm just not buyin that. The stars and other solar systems are all around us so if it were some flat plane wouldn't we all line up on this plane.I'm also not buyin into this " The universe is non-ending" Let's look at the universe from a different perspective shall we. How about we go micro for a minute. If we all lived on this tiny micro universe and we were just a speck of existence thorough the micro universe we would be oblivious to our known universe. I know I'm kinda hard to follow but stay with me. We are but a spec of dust on the edge of a remote solar system pee ons away from anything that vaguely close to us. Who's to say we are not apart os some tiny micro organism flowing through some vast openness and this black hole is just some vent. I think we as humans think too highly of our existence but Kinda like the drain thing going on there keep up with that.

Answer 5

Consider a two dimensional universe. Use the third dimension (that our brains can visualize) as a measure of gravitational force. So if there was no gravity in a region, the 2D universe would be modeled as a flat plane with no variation in the third D.

A block hole, then is a place where gravity goes to infinity, so the surface around it would be stretched in the third D to infinity.

Once you have mastered imagining a 2D universe, you can then begin to start on a 3D universe with a forth D needed to capture the force of gravity.

Oh well, I tried...

Answer 6

I see it as a black on black slowly swirling spot in the universe.
Sort of a fish eye view. Thats how my brain has to visualize it.
And as for where the matter goes, Couldn't it be recycled into new planets in a dimension we can not see.? Is it still there in a from we can't see or track with our current level of tech?
This question generates more questions than answers.....lol

Answer 7

If you thought of the sun as a bowling ball and the earth as a marble and place them on a mattress which represents space-time, you can see the effect that gravity has.

Now if you had something that was so heavy and small (dunno a hunk of depleted uranium) that would warp the fabric and tear the mattress, that would be a black hole.

That how's I understand it.

Answer 8

try to think about the universe more like a raisin, a black hole just cuts thru on one side of a ripple then opens up on the other side.