First let me say as a newbie, you guys (and gals!) have been great! Very patient, polite and helpful. Sincerly, thanks.
And I hope I’ve followed proper form by starting this thread and not hi-jacking the other BH thread (mod input would be appreciated on this).
…got me to thinking about how it’s a 2-D model. I’ve read some 'Relativity" and I’ve never seen this addressed - In real life where does the black hole ‘warp’ space into? Not north, south, east, west, up or down and that pretty much covers the 3 spatial dimensions. So does anyone know?
Does that make sense? We’ve all seen the ‘animations’ on ‘Nova’, PBS, etc of black holes that look like big funnels floating in the universe, but they wouldn’t really, would they? They should be symetrical - sucking matter in from all sides equally, not just from the the top of the ‘funnel’. Wouldn’t the event horizon actually be a sphere? But, wait, it couldn’t be…an inside-out sphere?
I must go lay down, I think I heard my brain snap…
This is a good question, since it’s an issue that confuses most people when they start to study General Relativity. It actually cuts directly to the heart of a subtlety in the way the theory is constructed. The crucial idea (due to 19th century German mathematician Riemann) is to find a way of talking about curved surfaces that only refers to the surface itself and not the space around it. A typical thought experiment about this is that surveyors can map out the shape of the Earth by measuring distances and angles between places on the surface. For instance, lay out a big triangle on the ground and measure the angles at its corners. On a flat surface we know that these should add up to 180 degrees. But, if your triangle on the Earth’s surface is big enough, you’ll find that they’ll actually add up to slightly more. You can thus establish that the Earth isn’t flat simply by moving about on the surface and making measurements. No need to fly off into space and look to see what shape it is.
Once you have a way of describing curved surfaces that doesn’t refer to the space around, you can just forget about that space. You can think about the surface entirely by itself. Now that’s near impossible to visualise (the rubber sheet is just an analogy and this is where it breaks down), but Riemann’s maths allow you to describe anything about the surface without having to do so. Since you don’t have to refer to the space around, you don’t have to say that the surface is warping “into” anything. It’s just warped. And GR is based on exactly this maths. Since there’s no need to talk about any space surrounding the curved surfaces that make up the 4D (the usual three, plus time) space in the theory, there’s no reason to believe it exists.
This may be a slightly different issue. Yes, the simplest black holes have spherical horizons. However, ones that exist in reality will be spinning and they’re a little more complicated in shape. Such holes also form what’s called an accretion disk outside their horizon: basically stuff falling in sort of queues up in a disk about the equator of the spinning hole before it reaches the horizon. Usually visualised as a sort of flat whirlpool. That’s probably what they were trying to animate.
I saw a program on PBS, about weather, that explained that you couldn’t actually see a tornado, only the debris it was throwing around. So you’re saying that, similarly, were you to throw a big dust cloud around an actual black hole, the dust would spin around in a flat plane, closer and closer to the ‘center’ and eventually disappear from site as it crossed the EH?
And anything coming at the black hole from a position tangent to the plane of the disc would first be drawn outward to the accretion disc before entering the BH itself?
Can you recomend a good book or two on Riemann math as it relates to relativity to further my understanding on this matter?
An object can enter a black hole from any which way, with or without being part a disk. It’s just that with most black holes we know of, most of the matter comes from the same plane. For instance, a stellar black hole might be part of a binary pair, and bleeding off material from its companion: In this case, the accretion disk will be in the plane of the orbit. There’s probably isolated black holes, as well, which don’t eat much of anything, and from no particular direction, but they’re much harder to detect. What we actually see is the matter getting heated up as it’s pulled in, not the hole itself (similar to your tornado example, I suppose).
Most popularisations merely mention the subject and then glide over it. On the other hand, introductions to Riemannian geometry naturally feature in any textbook on GR. Best option for a beginner is probably to start with the
Scientific American book (can’t recall the title - anyone else ?) co-authored by John Wheeler that assumes no backgound, but emphasises the geometry. If that’s too low level, then Wheeler’s Space-Time Physics (with Taylor) is an undergraduate level introduction to relativity, with equations but also a clear emphasis on the ideas.
