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Black Hole's "Point of No Return" Found
dsinc writes "Using a continent-spanning telescope, an international team of astronomers has peered to the edge of a black hole at the center of a distant galaxy. For the first time, they have measured the black hole's 'point of no return' — the closest distance that matter can approach before being irretrievably pulled into the black hole. According to Einstein's theory of general relativity, a black hole's mass and spin determine how close material can orbit before becoming unstable and falling in toward the event horizon. The team was able to measure this innermost stable orbit and found that it's only 5.5 times the size of the black hole's event horizon. This size suggests that the accretion disk is spinning in the same direction as the black hole. The observations were made by linking together radio telescopes in Hawaii, Arizona, and California to create a virtual telescope called the Event Horizon Telescope, or EHT. The EHT is capable of seeing details 2,000 times finer than the Hubble Space Telescope."
What in the name of everything you hold holy were you thinking when posting this?
Sure, the news is interesting, but while we're getting used to spelling errors and broken links on the front page, a blatantly mis-formatted link is something new, I think.
If you're too lazy to cut and paste. :)
http://news.harvard.edu/gazette/story/2012/10/point-of-no-return-found/
"Knock the stones together, guys!"
What is the difference between Event Horizon and Innermost Stable Orbit?
Imagine you are on a starship and have to pass near a black hole.
You read up the facts from the books and set your course.
5.5 times the size of the black hole's event horizon seems rather risky.
I would take 3 times the suggested distance to pass safely.
I'll keep that in mind next time I pilot my starship past one.
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In Newtonian gravity, 2-body orbits are stable, unless there is drag or some other non-gravitational force.
In General Relativity, orbiting bodies emit gravitational radiation, which carries away orbital energy, and so no orbit is truly stable. However, this only really becomes important near a neutron star or (even more so) near a black hole, where the gravitational radiation energy loss can be significant, and objects can spiral into each other fairly rapidly.
Of course, in either theory, the question of the stability of 3 or more body orbits is very complicated, and still an open area of research, but suffice it to say that N >2 body orbits need not be stable, although ejection of orbiting material is more likely than capture by the central body.
I regard this as basically a red herring, not to mention mixing up two different things.
The epicyclic frequency and disk stability has to do with the fluid dynamics of an accretion disk - that kind of stability does not require a black hole (look at Saturn's rings, which also have sharp edges).
The key word in Innermost Stable Circular Orbit is "stable" - the meaning is not that this orbit is not decaying (it is), but that it is stable to small perturbations. Inside the ISCO, a small perturbation will cause big changes, and the orbit will rapidly decay. So, outside the ISCO, the orbit is slowly decaying - "inspiraling" - while inside the ISCO, the orbit will decay very rapidly (i.e., "plunge" into the black hole). But, still, if you had a super-duper rocket, you could escape to infinity from inside the ISCO, as long as you hadn't crossed the event horizon.
All of this ignores tidal deformations, which convert orbital energy into heat and can also rapidly decay orbits.
Comment posting limits (and time...) won't let me respond to many individual comments, so I will see if I can address a few things at the same time here.
For a given angular momentum of something going around a black hole, you can work out what potential energy it would have at different radii. In a normal Newtonian case, you can think of having some satellite orbiting at some speed. If you try to push that satellite further in, while still maintaining its angular speed, it will try to pop back out since it is essentially going too fast to orbit at a smaller radius. There is a minimum in the potential energy of the satellite where it would have a circular orbit for that given angular momentum, as it would just stay at that radius. The potential energy about this radius would be like a bowl, if you push the satellite inward, it would roll back down toward the radius corresponding to a circular orbit. Momentum would of course carry it beyond that point, so it would oscillate in radius between some place closer and some place further from the circular orbit. This would give you an elliptical orbit where the radius goes between two values. The potential energy for over radius for a given angular momentum would look roughly like the red curve in the image here.
Now, for a black hole, GR gives some differences from Newtonian gravity when you get closer. The potential energy curve now looks more like this. There is still a stable orbit, as you can see it could oscillate around the minimum there like a marble in a bowl. In other words, small pushes on a perfectly circular orbit will turn it into a slightly elliptical orbit that is still pretty close to the circular one. However, if you push it far enough inward to get over that bump, the orbital radius would be like a marble just rolling down that hill toward the black hole. Now, the size of that bump changes depending on what angular momentum you are talking about. As you increase the angular momentum, which in Newtonian gravity would just give you a smaller radius for a circular orbit, that bump gets smaller. There is a point where the bump goes away, such that you just now have a curve that decreases with decreasing radius. Hence, a particle in such an orbit would continue to move closer to the black hole, as there is lower potential energy the closer it gets.
This is all due to the geometry of space around a black hole. Weird stuff like the circumference of a circle not being 2 pi r depending on how you measure the r from the black hole, which is why orbits no longer have the same stability they have in Newtonian gravity. This is not an effect due to gravitational waves. The orbiting particle can be something like a proton where the gravitational waves would be too small to matter. However, if you are talking about the orbit of a massive object, like a star or second black hole, then the gravitational waves become significant. In that case, the orbit at any radius would slowly decay due to emitting gravitational waves. Once the decay orbit hits the radius of the innermost stable orbit, the decay would greatly accelerate.
This is also not an effect of rotation or frame dragging, as it happens with a non-spinning black hole solution too. However, spinning black holes and frame dragging do factor into it, such that for a spinning black hole, the inner most stable orbit is smaller if you are going in the right direction around the black hole. Although there are other effects that the frame dragging causes. You get things like the ergosphere, a region where due to frame dragging, you would have to go faster than light to look stationary from an outside viewer, so all matter within that region is spinning around the black hole.
This is also quite distinct from the event horizo
The harvard.edu news article, quoted in the slashdot summary is inaccurate. It says:
This reads as a claim that they've resolved the event horizon. That's not true, although there are good prospects for resolving the event horizon of a black hole in the near future.
As is made clear in the rest of the article, and in the abstract of the published paper, what they've really resolved is structure inside the innermost stable circular orbit (ISCO).
In units where G=1 and c=1, the radius of the event horizon is 2M, where M is the mass of the black hole. The radius of the ISCO, for a nonrotating black hole, is 6M, i.e., three times the radius of the event horizon. What they've resolved is structure at 5.5M.
The first author of the paper, Doeleman, seems to post all his papers on arxiv.org, but unfortunately this one doesn't seem to be there yet, and Science has their copy paywalled.
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