Black Holes - the two points of view.

Naty1

Here are some other explanations and points of view....I have saved these in my notes from other discussions in these forums.

As Wald says, .
I posted this previously ...I believe it's Brian Greene or Kip Thorne
I believe this to be a precise description of an idealized model. It seems inconsistent with DrGreg's post :

which I believe is correct in a real world...a lumpy,curved spacetime not in our idealized
models...but that is a GUESS on my part.

DrGreg

I think you would gain much by studying Rindler coordinates and Rindler horizons. Virtually all of the weird properties of a black hole's event horizon are also properties of a Rindler horizon that is caused simply by the acceleration of an observer in empty space. In my view, Rindler horizons are easier to understand than black hole horizons because if you get confused you can always transform back into standard Minkowski SR coordinates to see what is "really" happening, so to speak. (Not that I am suggesting there is anything "unreal" about using other coordinates.)

Others have already given you several places to look. If those aren't enough you could also look at my own contributions in previous threads, e.g.
Stupider-er Twins Question
about the Rindler metric
Questions about acceleration in SR, post #13 onwards

Sagan and Ferris are correctly describing the mathematical model for an object of negligible mass (compared to a black hole) falling into a black hole of constant mass (i.e. whose mass doesn't increase due to absorption of other matter or decrease due to Hawking radiation). That wasn't what I was talking about.

Naty1

Mike...really good discussions so far here.....

My posts above and others have already answered..but I can offer a bit more. Schwarzschild coordinates include a flat asymptotic spacetime [that's not realistic]; FLRW assumes a perfectly homogeneous and isotropic spacetime and everyone here agrees the FLRW model does NOT apply to galactic scales....One has to also wonder how precise it is on cosmological scales...but that is not especially important for this discussion.

My reading SO FAR leads me to conclude there are not more exact formulations....we don't know how to solve EFE equations in an irregular, curved and lumpy spacetime.


Mike: You might find this in Wikipedia an interesting adjunct to Kip Thorne's description {I looked it up to get insight on what Kip Thorne meant}:

http://en.wikipedia.org/wiki/Eddingt...in_coordinates
where it points out:

.....

So while there is a type of time 'singularity' at the Schwarzschild radius, uniqueto those coordinates, I can think of three cases where it is NOT present: a free falling observer in those SAME coordinates, in the Eddington-Finklestein coordinates, and as I think has already been mentioned in this discussion, Kruskal-Szekeres coordinates.

So my own {novice} view is that between the different coordinate dependent descriptions and local versus global considerations, I have not yet come across any single, universal
all encompassing perspective that is absolute.

DrGreg

I have to confess that the dynamic formation of black holes isn't my area of expertise -- there are others on this forum who have explained this in greater depth in previous posts -- but I believe it is a consequence of Birkhoff's theorem.

Naty1

Mike,
There is a closely related discussion here which you might find interesting:

Unruh effect and lessons regarding reality
http://www.physicsforums.com/showthread.php?t=625633

[I'm pretty sure this was previously blocked......anyway, now is open again as I post here.
"reality" is a not a good word to bring up as it quickly devolves into philosophy.]

The essence of this discussion revolves around that fact an an inertial observer and an
accelerating observer have different spacetimes,one flat, one curved, hence different apparant degrees of freedom, hence different observations. What this actually means appears open to some debate....

Sound familar???

Naty1

You can get some insights into this, although no mathematics, from BLACK HOLES AND
TIME WARPS, by Kip Thorne....

I'll post if I can find it....

As I recall from other sources, the original horizon description is now called 'apparent' Horizon as discovered by Roger Penrose; Stephen Hawking did not like that coordinate dependent description, especially it's instantaneous discontinuous jumps when matter/energy was absorbed, and developed a complementary viewpoint, I believe the one routinely utilized today, the absolute horizon...

Others in these forum have discussed further distinctions, and one of them is that the [apparent] horizon jumps in anticipation of matter crossing the horizon. I believe this is analogous to the instantaneous appearance of the apparent horizon during the initial formation of a BH when it appears and cloaks the singularity; in contrast, Hawking's absolute horizon is created at the center of a new forming BH and moves smoothly to the stars surface as it impodes meeting the apparent singularity at the Schwarzschild radius.

Mike Holland

Naty1 and Greg, I really appreciate the time you have put in to try and educate me, but I remain unconvinced. I have read Kip Thorne’s book, and am very aware of his dilemma - after mentioning all the calculations I quoted, he concludes that Black Holes would take an infinite time to form, and then he gets on to Wheeler, and decides to suppress that thought and go along with majority opinion.

I am very aware of the relativity of realities. The fact is that a spaceman falling into a Black Hole REALLY DOES fall in in a short time, in HIS time frame, but he REALLY DOESN’T in OUR distant observer frame. Neither view is an illusion. Neither “appears to”. They are both valid descriptions of what REALLY happens.

Birkoff’s Theorem proves that the space outside a spherically symmetrical Black Hole follows Schwarzschild’s metric, and EVERY calculation using Schwarzschild’s metric has given the same result. The calculation has also been done for spinning Black Holes, but I cannot recall the reference.

Eddington-Finklestein coordinates also resolve to Schwarzschild coordinates outside the event horizon, so they make no difference.

As an example of where Kip Thorne gets it wrong,
The best physical interpretation is that, although we can never actually see someone fall through the event horizon (due to the infinite redshift), he really does. As the free-falling observer passes across the event horizon, any inward directed photons emitted by him continue inward toward the center of the black hole. Any outward directed photons emitted by him at the instant he passes across the event horizon are forever frozen there. So, the outside observer cannot detect any of these photons, whether directed inward or outward.

“Really does”? This assumes one frame is valid and the other an illusion, and that is rubbish. He then describes the observed redshift as purely resulting from the difficulty photons have escaping, and totally ignores the gravitational time dilation.

Naty1, you say

Schwarzschild coordinates include a flat asymptotic spacetime [that's not realistic]; FLRW assumes a perfectly homogeneous and isotropic spacetime and everyone here agrees the FLRW model does NOT apply to galactic scales....One has to also wonder how precise it is on cosmological scales...but that is not especially important for this discussion.

So many replies say the Schwarzschild solution is not accurate, but no one has proved that it gives the wrong answer, or shown me another one which can be proved to be more accurate and gives a different result for gravitational collapse. As I understand it, Schwarzschild only requires that the spacetime be flat and asymptotic at infinity. I doubt that Earth’s gravity and movement would affect the calculation. I’m beginning to think the only reason for rejecting the Schwarzschild calculations is that they say Black Holes don’t exist (at least not yet, in our time frame).

When describing Event Horizons expanding, one must always remember what space-time frame you are using. These events may occur locally, but gravitational time dilation means that in a remote time frame time is stopped at the Event Horizon. This means nothing happens. If you don't accept this, then you need to provide another equation relating time dilation to gravity near a Black Hole.

Mike

PeterDonis

Sorry, I lost track of this thread for a while so I am catching up with my responses:

No, you didn't, at least not when you claim that black holes do not exist. That is not what the mathematicians said.

Here's what Landau and Lifschitz said, that you quoted:

“According to the clocks of a distant observer the radius of the contracting body only approaches the gravitational radius as t -> infinity.”

That does *not* say that the black hole does not exist. It only says something about the clocks of the distant observer. If you look at all the other quotes you gave in context, they all say the same thing. None of them say that the black hole does not exist. In fact, the Oppenheimer-Snyder paper from Physical Review, that you quoted, explicitly says, IIRC, that there is a region of spacetime inside the horizon, and that the collapsing matter falls through that region to a curvature singularity at r = 0.

The error isn't between their math and their conclusions, it's between their math and *your* conclusions. *They* didn't conclude that the black hole doesn't exist. Only you are concluding that.

PeterDonis

Please give the exact chapter and verse for this. I've read Thorne's book too, multiple times, and I don't remember reading this. I remember him saying that, *from the viewpoint of the distant observer*, the BH takes an infinite time to form; but that is *not* the same as saying the BH takes an infinite time to form, period. Nor is it the same as saying the BH does not exist.

Again, please give exact, specific quotes and references. I don't know what you are referring to here; AFAIK Thorne's opinion about BH spacetimes has not changed significantly since the publication of MTW in 1973, at least, and probably well before that. The book you're referring to was published in 1993.

I don't agree with this way of putting it; or at least, it seems like a very unusual use of the words "real" and "reality". The BH spacetime is a single, geometric object; either it includes a region below the horizon, or it doesn't. The fact that the distant observer can't *see* the region below the horizon doesn't mean it isn't there.

Yes, if you mean the result that there is a region of the spacetime below the horizon. Every calculation has indeed shown that.

No, it doesn't. It means the distant observer can't *see* the region below the horizon. That's all it means. Why is that a problem?

"Gravitational time dilation" is just another way of saying that the photons take a long time escaping.

No, it doesn't. It means the coordinates used by the distant observer can't *describe* what happens (because they are singular at r = 2m), but that doesn't mean nothing happens. For example, Eddington-Finkelstein coordinates, which you have mentioned, are not singular at r = 2m, and they say things *do* happen there. Which, btw, is perfectly consistent with the fact that E-F coordinates give the same results as Schwarzschild coordinates when r > 2m, i.e., in the region where Schwarzschild coordinates are not singular.

DaleSpam

This is correct. There are relatively few exact solutions to the EFE. But you can always solve them numerically for irregular, curved, and lumpy space times.

harrylin

I think that the following has been cited twice here, but it doesn't make any sense to me:

“What would happen if you fall in? As seen from the outside, you would take an infinite amount of time to fall in, because all your clocks – mechanical and biological – would be perceived as having stopped’' - Carl Sagan “Cosmos”, 1981

I would think that if I (being "outside") perceive that your clocks stop due to your speed and gravitational potential far away from me, this has no effect whatsoever on my clocks. Thus it can have no effect on the Earth time that I estimate it will take for you to fall in. And inversely, for you it will look as if you faster and faster accelerate into the black hole - the final descent happens in nearly no proper time.

If anyone can explain my misunderstanding, I would be very grateful.

DrGreg

If I'm falling into a black hole in a finite time according to my own clock, let's say my clock reads exactly 4 pm at the moment I cross the event horizon. If you, hovering at a great constant height, are watching me, you'll see my clock approaching 4 pm, but it will keep slowing down and never actually reach 4 pm. And if you haven't seen my clock reach 4 pm, then you can't have seen me cross the event horizon.

Unless I've misunderstood your question, that's all there is to it, isn't it?

harrylin

OK I misunderstood what Hawkins meant with "“what would happen" - so he was talking about what, in theory, a distant observer literally might see - thanks for the clarification!

DrGreg

Well, it's not clear whether Sagan was referring to the time that you see an event or the time coordinate that you assign to the event, but the same logic applies either way.

harrylin

Ah yes, Sagan and not Hawkins! However, the difference between what one sees (an astronaut ever slowly disappearing near a black hole?) and what one infers from that (an astronaut fell into a black hole?) can be huge.

Mike Holland

Harrylin, you cannot at any stage "infer" that DrGreg fell into the black hole. After carrying out his researches very close to the Event Horizon he might have fired his rockets and come back to join us for tea and to discuss his observations.

Only when he falls through the EH can he say it has happened. But we cannot translate this event into our coordinate system (time frame) because we land up with t = infinity. So we external observers can never say something has fallen into a Black Hole, only that it will, and that it does in its local timeframe.


Yes, but be careful with "seen me". It can lead to confusion. If you hover close to the EH, we will see you time dilated, and this has nothing to do with the time photons take to escape the gravity - it depends purely on your distance from the EH. As you fall in photons will take longer and longer to escape, and this causes an additional "apparent" redshift superimposed on the gravitational redshift. Many writers get mixed up with these two redshifts, and conclude that the time dilation is an illusion.

Now if you take this a step or two further, we find that Xwatl, from the planet Wortl, who started falling intro a Black Hole 10,000 years ago, also hasn't reached the EH in our time frame, and neither has that gas cloud that the BH started eating a billion years ago. In fact, nothing has ever falllen into a Black Hole, in our timeframe, so we can never say it has happened.

Mike

PAllen

"our coordinate system" is a convention. Numerous times it has been explained there is nothing physically preferred about SC coordinates. Using a different simultaneity convention, an outside observer can specify a specific time of event horizon crossing even though they never 'see' the crossing. Do you really think a rocket accelerating at 1 g must conclude that much of the universe has ceased to exist? But you say they can stop accelerating. Well, any accelerating hovering observer can choose to stop at any time - and find the part of the universe on the other side of the horizon.
This is pure and simply wrong. There are not two red shifts - period; mathematical fact. The time dilation and the slow speed of photon escape and the redshift are all manifestations of exactly the same factor in the metric, not additive phenomena. All of the authors you misinterpret understand this. Find one author or any mathematical justification of additive redshifts for this situation.
In GR, frames are local and coordinates are arbitrary. This is fundamental fact of GR that you reject - and despite your misinterpretation, all the authors you cite did understand this.