Black Holes - the two points of view.

[Mike Holland]

I wish to take up a discussion between Elroch and DrStupid in RossiUK’s topic “First Post – a question about Black Holes and Gravity”. My post is essentially an exposition of Elroch’s view, which I have shared for many years. Elroch’s exposition was very sedate, and I feel it needs to be shouted from the rooftops - “There are no Black Holes in this universe”. Well, not quite, anyway!

When discussing black holes, there are basically two points of view, that of a remote observer and that of the poor spaceman who falls into one. The difference is caused by gravitational time dilation. From the remote viewer’s point of view (or in his time frame, if you prefer), the passage of time is retarded near the black hole, and comes to a complete stop at the Schwarzschild Radius. So as far as this remote viewer is concerned, a falling spaceman would never reach the Schwarzschild radius, but would hover just outside it gradually edging closer and closer. But the spaceman, in turn, will have a very different experience, falling past the SR in a very short period of time according to his clock.

The consequence of this is that as far as outside observers are concerned, the spaceman never enters the black hole. And neither does any other falling matter. Nothing has ever fallen into a black hole as far as our clocks are concerned!

But extreme time dilation would exist for a collapsing star even before it reaches the black hole state. A super-massive collapsing object which is nearly a black hole would itself be highly time dilated (by our clocks), and the collapse process itself would slow down and come to a complete stop just as it reaches black hole status - which would only happen when our clocks read infinity.

NB. Schwarzschild radius and Event Horizon are not the same thing. Every mass has a Schwarzschild radius within it, and only when all the mass is compressed within this radius would an Event Horizon form.




Many prominent astrophysicists who have performed the calculations support these conclusions:

“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

“ .. a critical radius, now called the “Schwarzschild radius,” at which time is infinitely dilated.”
- Paul Davies “About Time”, 1995

“From the standpoint of an outside observer, time grinds to a halt at the event horizon.”
- Timothy Ferris “The Whole Shebang”, 1997

“The closer we are to the event horizon, the slower time ticks away for the external observer. The tempo dies down completely on the boundary of the black hole.”
- Igor Novikov “The River of Time”, 1998

“When all thermonuclear sources of energy are exhausted a sufficiently heavy star will collapse. This contraction will continue indefinitely till the radius of the star approaches asymptotically its gravitational radius.”
- Oppenheimer and Snyder “Phys.Rev. 56,455” 1939

“According to the clocks of a distant observer the radius of the contracting body only approaches the gravitational radius as t -> infinity.”
- Landau and Lifschitz “The Classical Theory of Fields”, 1971

“What looks like a black hole is “in reality” a star frozen in the very late stages of collapse.”
- Paul Davies “About Time”, 1995

“At the stage of becoming a black hole, time dilatation reaches infinity.”
- Jayant Narlikar

In all his writings, Fred Hoyle referred to them as “near black holes”, while the Russians called them “frozen stars”..


All the mathematicians who have solved Einstein’s equations for a collapsing super-massive body have come to the same conclusion - in the reference frame of any external observer, it takes an infinite time for a Black Hole to form. This means that there are no Black Holes in the universe, and won’t be until the age of the universe is infinity!

I have seen arguments that these calculations were all done for a distant observer in the “proper time” of the Black Hole. Proper time means that the observer is motionless relative to the BH, and nowhere near any gravitational mass which could affect his clock. But this condition was used simply to simplify the mathematics. We can calculate the effect of our relative motion, which is hardly relativistic, and Earth’s gravity, which is so infinitesimal it can only be measured with atomic clocks, and these factors have no significant effect on the results of the calculations.

The time dilation around a collapsing super-massive object only becomes significant extremely close to the Schwarzschild radius and so for all intents and purposes such an object would be indistinguishable from a Black Hole. But perhaps one difference is the magnetic fields that have been observed around some supposed Black Holes in other galaxies, indicating that they are not quite there yet.

What we end up with is an object collapsing more and more slowly as it tries to fit within its Schwarzschild radius, and this almost Event Horizon area becomes extended as more material falls onto it. The almost-EH is not a surface, but a whole volume of the collapsing mass, with never enough mass within its Schwarzschild Radius to actually form an event horizon. So we don’t have an expanding Event Horizon as matter falls in, we have an expanding region of “almost Event Horizon”, with the inner regions being compressed ever closer to forming a Black Hole.

But what about the other point of view, that of the poor spaceman who is falling into such a super-massive object as at collapses into a Black Hole? He will see an almost-Black –Hole ahead of him as he approaches. It only becomes a BH for him when he arrives there. If he could hover close to the object (rockets blasting like anything to keep him there), then he would see the outside universe speeded up, just as we see clocks in orbit above the Earth running faster. But as he is accelerating under the gravitational attraction, the converse happens, and he will actually see our clocks slowed down. Counter-acting the gravitational speed-up of our clocks, from his point of view, are apparent time dilation effects due to the time our photons take to reach him as he speeds up.

From his point of view, he will approach the speed of light as he approaches the Black Hole to be. But our view is different. We see him accelerating until he is about twice the Schwarzschild Radius away, and then time dilation takes over and he slows down and in fact never gets there. If he was hovering, we would simply see him gravitationally time dilated. But as he approaches the SR, photons take longer and longer to escape and this gives rise to another, optical, time dilation. This apparent time dilation is added to the GR dilation making him appear even more frozen in time.

When he reaches the Schwarzschild radius, along with all the other collapsing matter, he does not travel any further because space and time are distorted in such a way that the distance between him and the centre becomes a time dimension. The singularity is in his future, not in any space direction. In effect, he is already at the centre and all the surrounding matter is collapsing in on him (OK, I expect a lot of controversy about this description!).

I have written this as though we could observe events all the way into the forming event horizon. But of course this would be impossible. Time dilation creates such a red shift that visible light will be stretched to into radio waves and beyond, making observation impossible. Also, any such collapsing mass would probably be surrounded by in-falling matter and by the radiation that it emits. So as far as observations are concerned, all the above probably makes no difference,.

My one concern with this description of events is that the dilation only becomes significant extremely close to the SR, and I don’t know what happens when one gets down to quantum dimensions. At one Plank length away from an Event Horizon of 10 km radius, the time dilation factor is about 10**19 to 1. Which rules at this scale? Quantum uncertainty or gravity? My money is on gravity, but I think a Theory of Quantum Gravity is required to resolve this issue.

Mike

 

[pervect]

There isn't any particular reason to favor the observer at infinity over the one who falls into the black hole.

THis becomes clearer if you consider the closely related example of event horizons, the Rindler horizon, which is caused by acceleration and is formally very similar to that of a black hole (except it's flat, not curved).

Suppose a rocketship accelerates at 1 gravity. About 1 year into their journey, they will see the Earth appear to fall into an event horizon, called the Rindler horizon.

The Earth will get redder and dimmer, and their clocks on Earth will appear to slow and stop according to the accelerating observer.

If we take the viewpoint of the accelerating observer as representing some "universal truth", we would say that "time stops on the Earth" and we might add "It stops in the year xxxx", where xxx is the year the Earth falls behind the horizon.

Which should be obviously silly, because the person on Earth won't even know anything happened.

Applying the same argument in this only slightly different situation shows how silly it is to give one particular observer "priveleged status" as far as existence goes. The observer at infinity might not be able to see certain events, but that hardly means that they don't happen, just as the rocketship observer's inability to see anything after some specific date on Earth doesn't mean that "it never happens".

 

[Mike Holland]

Pervect, I don't recall saying at any stage that one observer is "privileged". My title says "two points of view", and that's what they are. All I am pointing out is that in "our" reference frame, some events take an infinite time, according to all the GR mathematicians, and therefore as far as we are concerned, they haven't happened. Doesn't mean they won't happen (after an infinite time).

We can only say something "has" happened when we can prove that it occurred before our present.

I read up on Rindler horizons several years ago, but don't remember much about them. Will have to look them up again. But do they prove that Oppenheimer, Snyder, Landau, etc are all wrong? If not, how do you make sense of my quotes from those guys?

Mike

 

[Mike Holland]

OK, I just calculated that 1 years acceleration at 1g = c. So the receding Earth's relativistic mass will have reached infinity, and it must have become a black hole shortly before that. But you cannot accelerate up to c, Special Relativity prevents that with time dilation, lorentz contraction, relativistic mass increase, etc, so the problem should never arise!
Mike

 

[Dale]

in the reference frame of any external observer, it takes an infinite time for a Black Hole to form. This means that there are no Black Holes in the universe, and won’t be until the age of the universe is infinity!

This seems to be your key thesis, and there are several things wrong with it.

First, the initial statement is not true for "any external observer", as claimed. It is only true for observers using Schwarzschild coordinates. External observers using other coordinates may disagree.

Second, the reference to "in the universe" is a coordinate independent reference to the manifold. The coordinate-dependent reasoning presented cannot be used to justify the coordinate-independent conclusion asserted. Just because something is not in a particular coordinate chart does not imply it is not in the manifold.

Third, the "age of the universe" is usually associated with the FLRW spacetime, not the Schwarzschild spacetime, so I am not sure what you actually intended to refer to there.

 

[PeterDonis]

Many prominent astrophysicists who have performed the calculations support these conclusions

You should be extremely careful about how much you read into pop-science statements about black holes, or indeed about any counterintuitive aspect of physics, even when they are written by world-class physicists. English, or any other natural language, is not well adapted to expressing scientific conclusions; it is very difficult to avoid drawing incorrect deductions from the English statements (see below for an example). That's why the real descriptions of our scientific theories, the ones we actually use to make predictions and test them, are written in mathematics, not natural language.

All the mathematicians who have solved Einstein’s equations for a collapsing super-massive body have come to the same conclusion - in the reference frame of any external observer, it takes an infinite time for a Black Hole to form.

Within the limitations of English, this is one way of stating what the math says. But you go on to draw an incorrect deduction from it:

This means that there are no Black Holes in the universe, and won’t be until the age of the universe is infinity!

This is *not* what the math says, and it is not correct. If you disagree, then please post the actual math (not English statements) that you are using to justify your claims.

Also, even given the limitations of English, you have some of the terminology wrong:

Proper time means that the observer is motionless relative to the BH, and nowhere near any gravitational mass which could affect his clock.

This is not what "proper time" means, not even in Special Relativity, let alone in General Relativity.

 

[Dale]

So the receding Earth's relativistic mass will have reached infinity, and it must have become a black hole shortly before that.

This is a common misconception. See the FAQ
http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

 

[Naty1]

All the mathematicians who have solved Einstein’s equations for a collapsing super-massive body have come to the same conclusion - in the reference frame of any external observer, it takes an infinite time for a Black Hole to form.

Hey Mike, interesting quotes...lots of perspectives...

Dalespam posts:

[The coordinate-dependent reasoning presented cannot be used to justify the coordinate-independent conclusion asserted. Just because something is not in a particular coordinate chart does not imply it is not in the manifold.
/QUOTE]

I'd even generalize this a bit further: Someone else mentioned Schwarzschild and FLRW coordinates and neither of those are EXACT models for our observations...so I would doubt
what appears as 'infinite time' in any such idealized model should be taken too literally.


The description I like is from Kip Thorne's in BLACK HOLES AND TIME WARPS:

Finkelstein's reference frame was large enough to describe the star's implosion ...simultaneously from the viewpoint of far away static observers and from the viewpoint of observers who ride inward with the imploding star. The resulting description reconciled...the freezing of the implosion as observed from far away with the continued implosion as observed from the stars surface...an imploding star really does shrink through the critical circumference without hesitation...That it appears to freeze as seen from far away is an illusion...General relativity insists that the star's matter will be crunched out of existence in the singularity at the center of the black...

I suspect we have lots more to learn about geometry, spacetime, horizons and particles!

 

[Naty1]

My one concern with this description of events is that the dilation only becomes significant extremely close to the SR, and I don’t know what happens when one gets down to quantum dimensions. ... Which rules at this scale? Quantum uncertainty or gravity? ...I think a Theory of Quantum Gravity is required to resolve this issue.

likely that could provide additional insights... but the singularity at the horizon is a coordinate singularity different from the singularity at the center of a BH where both relativity and QM diverge...In other words, the horizon time divergence is Schwarzschild dependent and disappears in other coordinates...This is analogous to the apparent horizon
of a constantly accelerating observer in Rindler coordinates in Minkowski space.

But as I posted in the prior note, it doesn't seem certain to me exactly what conclusions can be drawn from these idealized models.

 

[pervect]

OK, I just calculated that 1 years acceleration at 1g = c. So the receding Earth's relativistic mass will have reached infinity, and it must have become a black hole shortly before that. But you cannot accelerate up to c, Special Relativity prevents that with time dilation, lorentz contraction, relativistic mass increase, etc, so the problem should never arise!
Mike

A better way to describe what happens is to use the relativistic rocket equation to plot the course of the rocket.

http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html has the formulae, converting them to latex they are:

<br /> t = \frac{c}{a} sinh \frac{aT}{c} = \sqrt{ \left(\frac{d}{c}\right) ^2 + \frac{2d}{a} }<br />
<br /> d = \frac{c^2}{a} \left( cosh \frac{aT}{c} - 1\right) = \frac{c^2}{a} \sqrt{1 + \left(\frac{aT}{c}\right)^2 - 1}<br />Here t is time as measured on earth, d is distance as measured on earth, and T is the proper time aboard the rocket.

You can consider a = 1 light year / year^2 to be 1 g - it's quite close, and the approximation I used when I made my remark.

If you plot the course of the rocket, you'll see though it never reaches the speed of light, it does accelerate fast enough that light signals emitted at a certain time from the Earth (the time when the asymptote of the hyperbola crosses the origin) will never catch up to it.

The problem with saying that the relativistic mass goes to infinity is that a) a correct relativistic analysis of the rocket reveals it never gets to 'c' and b) you can't compute gravity by putting "relativistic mass" into Newtonian formulae.

[add]Plus the point that Doctor Gregg made.

If you want to adopt the rocketship's point of view, you say that the metric coefficient of g_00 goes to zero and forms and event horizon, the Rindler horizon, behind the rocketship.

Greg Egan has a webpage on the Rindler Horizon for sure, it might be a bit advanced though.

 

[DrGreg]

THis becomes clearer if you consider the closely related example of event horizons, the Rindler horizon, which is caused by acceleration and is formally very similar to that of a black hole (except it's flat, not curved).

Suppose a rocketship accelerates at 1 gravity. About 1 year into their journey, they will see the Earth appear to fall into an event horizon, called the Rindler horizon.

The Earth will get redder and dimmer, and their clocks on Earth will appear to slow and stop according to the accelerating observer.

OK, I just calculated that 1 years acceleration at 1g = c. So the receding Earth's relativistic mass will have reached infinity, and it must have become a black hole shortly before that. But you cannot accelerate up to c, Special Relativity prevents that with time dilation, lorentz contraction, relativistic mass increase, etc, so the problem should never arise!

Mike, this has nothing to do with the Earth's mass or it's gravity. The same effect occurs even if Earth is not there, i.e. if you accelerate at 1 g in empty space, with no gravitational sources nearby, an "apparent horizon" forms (immediately) at about 1 light-year behind you which behaves almost identically to the event horizon of a black hole as observed by a hovering observer. Nothing, not even light, can pass through the horizon towards you, and objects "dropped" towards the horizon take an infinite time, according to you, to get there. However, from the point of view of any inertial observer, the location of your "horizon" is no different than anywhere else in empty space, and the dropped objects pass through it with no problem.

 

[pervect]

Pervect, I don't recall saying at any stage that one observer is "privileged". My title says "two points of view", and that's what they are. All I am pointing out is that in "our" reference frame, some events take an infinite time, according to all the GR mathematicians, and therefore as far as we are concerned, they haven't happened. Doesn't mean they won't happen (after an infinite time).

No, assigning an event an infinite time coordinate doesn't mean that it "didn't happen". In general having an infnite coordinate value is reason for concern, but it doesn't "prove" anything.

There is an opportunity here though, inspired by your title "two points of view". The opportunity here is for you to learn that the concept of "Now" depends on the observer - that it is not a universal concept.

This is just a rather extreme example, whereby one observer's notion of "now" is at future infinity for another observer.

 

[DrGreg]

But extreme time dilation would exist for a collapsing star even before it reaches the black hole state. A super-massive collapsing object which is nearly a black hole would itself be highly time dilated (by our clocks), and the collapse process itself would slow down and come to a complete stop just as it reaches black hole status - which would only happen when our clocks read infinity.

NB. Schwarzschild radius and Event Horizon are not the same thing. Every mass has a Schwarzschild radius within it, and only when all the mass is compressed within this radius would an Event Horizon form.

The Schwarzschild coordinate description is an idealised version of something that doesn't happen in practice. It's a good approximation in many ways but has some flaws. In particular it assumes a black hole's mass remains constant, implying it has existed for an infinite time in the past and will continue to exist for an infinite time in the future. It doesn't account for a black hole gaining mass from in-falling matter or losing mass via Hawking radiation. Also any analysis of the behaviour of matter near a Schwarzschild black hole ignores any gravitational effects due to the matter itself.

To a distant observer, a black hole surrounded by a shell of matter (outside its Schwarzschild radius) behaves identically to a black hole that has absorbed that matter. Strange though it may seem, matter outside the Schwarzschild radius can cause the Schwarzschild radius to increase. I think I am right in saying that matter can actually be absorbed by an expanding event horizon within finite time according to a distant hovering observer.

 

[Mike Holland]

Well, that’s a whole lot of responses to reply to. Guess I asked for it! So here goes…

Dalespam, to your knowledge has the collapse of a super-massive object ever been computed using a different coordinate system? And if so, did the results disagree? You are just supposing that they “may” disagree. Please let me know of other coordinate systems that have been used for the calculation.

OK, I used the term “universe” rather loosely. Using your term, I should say that there are no black holes in our coordinate chart. One cannot convert an event (x,y,z,t) at a black hole to an (x,y,z,t) in our coordinate system without infinities appearing.

I thought the age of the universe was 13.7 billion years. Is it different in a Schwarzschild coordinate system?

I haven’t read the FAQ on Rindler horizons yet. Give me a few days to catch up.

PeterDonis, I am surprised you regard “The Classical Theory of Fields” and Physical Review as pop-science articles. I did not draw incorrect deductions. I simply quoted the deductions of the mathematicians. Please show me where I have misinterpreted the conclusions of Landau and Lifschitz, for example, quoted above.

“This is *not* what the math says, and it is not correct. If you disagree, then please post the actual math (not English statements) that you are using to justify your claims.”
Rubbish. The maths is written out in Landau and Lifschitzs’ book on pages 297 to 299. Please tell me where the error is between their maths and their conclusions.

Naty1, I have Kip Thorne’s book next to me, and he says that in Finklestein’s solution, the geometry outside the imploding star is that of Schwarzschild (top of page 246), so as far as the external observers are concerned, the results will be the same. You suggest that Schwarzschild and FLRW coordinates are not EXACT models. What evidence? And are there any more exact formulations!

Pervect, I had assumed that as the rocket man never reaches c, so the Rindler horizon would never quite form. You are telling me that this is incorrect, so as I mentioned to Dalespam, I have some reading to do.

‘No, assigning an event an infinite time coordinate doesn't mean that it "didn't happen". In general having an infnite coordinate value is reason for concern, but it doesn't "prove" anything.’

Not true. Just go back a step to before he reached the EH. According to GR, when we look at the falling spaceman today, he is a meter away from the EH. We come back in a year’s time and he is a centimeter away. Another thousand years and he’s down to 1mm, etc. OK, we can’t really see him when he is this close, but GR gives us the equation to calculate his position. We don’t have to use the word “infinity”, Just the fact that he approaches the EH asymptotically in time means it hasn’t happened yet in our timeframe.

I know what is meant by “now” for an observer. In a theoretical sense it is a line drawn vertical to his world line, but in a practical sense it is the light cone that he is at the apex of.

DrGreg, I understand the effect of acceleration. It just the same as standing in a gravitational field and clocks above you go faster than yours while those below go slower (except that it would have to be a linear grav field to be fully equivalent). I am a great believer in Einstein’s equivalence principle, and always try to look at thing from both points of view. But I’m going to have a hard time trying to reconcile all my quotes above with Rindler horizons forming. Give me a while to work on it.

“To a distant observer, a black hole surrounded by a shell of matter (outside its Schwarzschild radius) behaves identically to a black hole that has absorbed that matter. Strange though it may seem, matter outside the Schwarzschild radius can cause the Schwarzschild radius to increase. I think I am right in saying that matter can actually be absorbed by an expanding event horizon within finite time according to a distant hovering observer.” - DrGreg

“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

“From the standpoint of an outside observer, time grinds to a halt at the event horizon.” - Timothy Ferris “The Whole Shebang”, 1997

Who do I believe? The only ones who have maths to back up their claims are Sagan and Ferris. All the maths I have seen disagrees with you.


Thanks all of you for your responses and attempts to educate me. Please keep throwing stuff at me – it keeps the old mind active!

Mike

 

[TMM]

I think it's the case that time dilation prevents you from ever seeing something reach the singularity. After all, as the mass M increases, the field strength at the event horizon is ~1/M, so we can make it as small as we like.

 

[Dale]

Dalespam, to your knowledge has the collapse of a super-massive object ever been computed using a different coordinate system? And if so, did the results disagree? You are just supposing that they “may” disagree. Please let me know of other coordinate systems that have been used for the calculation.

As far as I know, the quotes you referred to are about the Schwarzschild coordinates, which can describe a small amount of matter falling into an already existing static black hole. In Schwarzschild coordinates a falling object goes to the event horizon as t goes to infinity. There are alternative coordinates for the Schwarzschild spacetime such as Gullstrand-Painleve, Eddington-Finkelstein, Kruskal-Szekeres, and Lemaitre coordinates.

http://en.wikipedia.org/wiki/Gullstrand–Painlevé_coordinates
http://en.wikipedia.org/wiki/Eddington–Finkelstein_coordinates
http://en.wikipedia.org/wiki/Kruskal-Szekeres_coordinates
http://en.wikipedia.org/wiki/Lemaitre_coordinates

I think that all of these remove the coordinate singularity in different ways, and they all have a falling object cross in a finite coordinate time.

OK, I used the term “universe” rather loosely. Using your term, I should say that there are no black holes in our coordinate chart. One cannot convert an event (x,y,z,t) at a black hole to an (x,y,z,t) in our coordinate system without infinities appearing.

Sure, but rather than "our" coordinate chart I would say "the Schwarzschild" coordinate chart. There is no reason that we have to pick any of the above charts as "ours".

I thought the age of the universe was 13.7 billion years. Is it different in a Schwarzschild coordinate system?

The age of the universe is a feature of the FLRW spacetime. It is a different spacetime than the Schwarzschild space-time, so you cannot get from one to the other with just a coordinate transform. The Schwarzschild spacetime is static, so there is nothing corresponding to an age.

http://en.wikipedia.org/wiki/Friedmann–Lemaître–Robertson–Walker_metric

 

[Nugatory]

Strange though it may seem, matter outside the Schwarzschild radius can cause the Schwarzschild radius to increase.

Can you point me to some references on this mechanism? It seems altogether plausible to me, but I'd expect that it takes more than the Schwarzschild solution (stationary solution doesn't leave much room for an increasing anything, vacuum solution only valid for negligible test masses outside the central singularity) to describe properly.

I think I am right in saying that matter can actually be absorbed by an expanding event horizon within finite time according to a distant hovering observer.

That also sounds plausible - it's hard to imagine what else could be meant by "an expanding event horizon".

 

[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,

"there appears to be no natural notion of a black hole in a closed Robertson-Walker universe which re-collapses to a final singularity", and further, "there seems to be no way to define a black hole in a closed universe, because it requires going to infinity, but there is no infinity in a closed universe."

a Schwarzschild singularity in a coordinate system doesn't necessarily represent a pathology of the manifold. (Consider traveling due East at the North Pole). Nevertheless, the fact that no true black hole can exist in a finite universe shows that the coordinate singularity at r = 2m is not entirely inconsequential, because it does (or at least can) represent a unique boundary between fundamentally separate regions of spacetime,
Let's take the simplest case, where the black hole is in asymptotically flat space-time. This will happen automatically if one uses the usual Schwarzschild metric

different frames see different things...analogous to length contraction and as mentioned above, and time dilation…. The proper time for a freely-falling observer to reach the event horizon is finite, yet the free-fall time as measured at infinity is infinite…The acceleration is due to depth of gravitational well - a global feature. The tidal forces due to gradient - a local feature.

, when we mention velocity, acceleration, etc, we need to be clear what is being measured relative to what, and whether it is a "proper" invariant measurement, or a local or remote coordinate measurement.

.

Hence it would appear that, in the falling frame, the observer should encounter an infinite amount of radiation in a finite time, and so be destroyed. On the other hand, the event horizon is a global construct, and has no local significance, so it is absurd to0 conclude that it acts as physical barrier to the falling observer.
Quantum Fields in Curved Space by Birrell and Davies, pages 268-269

I posted this previously ...I believe it's Brian Greene or Kip Thorne

We found earlier that the Schwarzschild metric has a coordinate singularity at the event horizon, where the coordinate time becomes infinite. Recall that the coordinate time is approximately equal to the far away observer's proper time. However, a calculation using transformed coordinates shows that the infalling observer falls right through the event horizon in a finite amount of time (the infalling observer's proper time). How can we interpret solutions in which the proper time of one observer approaches infinity yet the proper time of another observer is finite?

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.

There's no coordinate-independent way to define the time dilation at various distances from the horizon—a clock is ticking relative to coordinate time, so even if that rate approaches zero in Schwarzschild coordinates which are the most common ones to use for a nonrotating black hole, in a different coordinate system like Kruskal-Szekeres coordinates it wouldn't approach zero at the horizon,

I believe this to be a precise description of an idealized model. It seems inconsistent with DrGreg's post :

I think I am right in saying that matter can actually be absorbed by an expanding event horizon within finite time according to a distant hovering observer.

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]

DrGreg, I understand the effect of acceleration. It just the same as standing in a gravitational field and clocks above you go faster than yours while those below go slower (except that it would have to be a linear grav field to be fully equivalent). I am a great believer in Einstein’s equivalence principle, and always try to look at thing from both points of view. But I’m going to have a hard time trying to reconcile all my quotes above with Rindler horizons forming. Give me a while to work on it.

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

“To a distant observer, a black hole surrounded by a shell of matter (outside its Schwarzschild radius) behaves identically to a black hole that has absorbed that matter. Strange though it may seem, matter outside the Schwarzschild radius can cause the Schwarzschild radius to increase. I think I am right in saying that matter can actually be absorbed by an expanding event horizon within finite time according to a distant hovering observer.” - DrGreg

“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

“From the standpoint of an outside observer, time grinds to a halt at the event horizon.” - Timothy Ferris “The Whole Shebang”, 1997

Who do I believe? The only ones who have maths to back up their claims are Sagan and Ferris. All the maths I have seen disagrees with you.

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...

Naty1, I have Kip Thorne’s book next to me, and he says that in Finklestein’s solution, the geometry outside the imploding star is that of Schwarzschild (top of page 246), so as far as the external observers are concerned, the results will be the same. You suggest that Schwarzschild and FLRW coordinates are not EXACT models. What evidence? And are there any more exact formulations!

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/Eddington-Finkelstein_coordinates
where it points out:

...In both these coordinate systems the metric is explicitly non-singular at the Schwarzschild radius

...

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]

Strange though it may seem, matter outside the Schwarzschild radius can cause the Schwarzschild radius to increase.

Can you point me to some references on this mechanism? It seems altogether plausible to me, but I'd expect that it takes more than the Schwarzschild solution (stationary solution doesn't leave much room for an increasing anything, vacuum solution only valid for negligible test masses outside the central singularity) to describe properly.

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
https://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 apparent degrees of freedom, hence different observations. What this actually means appears open to some debate...

Sound familar?

 

[Naty1]

Strange though it may seem, matter outside the Schwarzschild radius can cause the Schwarzschild radius to increase.

Can you point me to some references on this mechanism?

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 into 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:

PeterDonis, I am surprised you regard “The Classical Theory of Fields” and Physical Review as pop-science articles. I did not draw incorrect deductions. I simply quoted the deductions of the mathematicians.

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

Please show me where I have misinterpreted the conclusions of Landau and Lifschitz, for example, quoted above.

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.

Rubbish. The maths is written out in Landau and Lifschitzs’ book on pages 297 to 299. Please tell me where the error is between their maths and their conclusions.

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]

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

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.

and then he gets on to Wheeler, and decides to suppress that thought and go along with majority opinion.

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 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.

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.

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.

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

As an example of where Kip Thorne gets it wrong,
...

“Really does”? This assumes one frame is valid and the other an illusion

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?

He then describes the observed redshift as purely resulting from the difficulty photons have escaping, and totally ignores the gravitational time dilation.

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

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.

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.

 

[Dale]

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.

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]

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.

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]

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?

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]

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!

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]

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.

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.

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.

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]

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.

"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.

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.

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.

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

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.

 

[Mike Holland]

There are two different redshift phenomena taking place. If a clock is hovering near the Event Horizon, we will see it ticking slowly, at a rate dependent on the size of the BH and its distance from it. Any photons leaving it will be delayed as they escape the gravity, but ALL the photons will be delayed the same amount as the clock is hovering at a fixed point in the gravitational field. So there is no redshift due to the photons taking a long time to get to us. They all take the same long time to reach us. The only redshift in this case is due to the clock slowing, ie. gravitational time dilation. I agree that in this case the gravitatiional time dilation and the slowing of escaping photons are all part of the metric.

If the clock falls into the gravity field, then successive photons take longer and longer to escape the increasing gravity, and this creates a redshift in addition to that of a hovering clock.

Do you believe that there would be a photon redshift when the clock is not moving? Or do you not accept that as the clock descends into the gravity field, emitted light gets delayed more and more?

OK, I agree that a complete mathematical analysis of the descent should cover both redshifts, but there are still two processes involved. For a falling body, successive photons take longer to be emitted because of the time slowing, and then, in addition, take longer to reach us when they have been emitted. Two steps which both cause redshift.

Mike

 

[PAllen]

There are two different redshift phenomena taking place. If a clock is hovering near the Event Horizon, we will see it ticking slowly, at a rate dependent on the size of the BH and its distance from it. Any photons leaving it will be delayed as they escape the gravity, but ALL the photons will be delayed the same amount as the clock is hovering at a fixed point in the gravitational field. So there is no redshift due to the photons taking a long time to get to us. They all take the same long time to reach us. The only redshift in this case is due to the clock slowing, ie. gravitational time dilation. I agree that in this case the gravitatiional time dilation and the slowing of escaping photons are all part of the metric.

If the clock falls into the gravity field, then successive photons take longer and longer to escape the increasing gravity, and this creates a redshift in addition to that of a hovering clock.

Do you believe that there would be a photon redshift when the clock is not moving? Or do you not accept that as the clock descends into the gravity field, emitted light gets delayed more and more?

OK, I agree that a complete mathematical analysis of the descent should cover both redshifts, but there are still two processes involved. For a falling body, successive photons take longer to be emitted because of the time slowing, and then, in addition, take longer to reach us when they have been emitted. Two steps which both cause redshift.

Mike

For anyone hovering or falling clock emitting light, there is one factor for both redshift and time dilation (rate of the image of the clock) as seen by a distant observer. You can choose to factor this into a gravitational component and a speed component, but this is only possible in ideal geometries that don't exist in the real universe. In fact, the time dilation between two distant locations is a non-physical abstraction. The only thing that is physical is the observation of the rate of clocks of known intrinsic rate - and this will always agree with the redshift factor.

 

[Dale]

Redshift is always calculated the same way: take two timelike worldlines, on one pick two nearby events, calculate the proper time between them, find a null geodesic from each event to an event on the other worldline, calculate the proper time between those, the redshift is the ratio.

This procedure works in flat spacetime, curved spacetime, with or without motion.

 

[Mike Holland]

The time a photon takes to reach us when the clock is at a particular distance from the EH is affected by the delay of the photon in escaping from the gravitational field. If the clock is falling, then, in addition to a SR effect from its speed relative to us, the photons will take longer and longer to escape from the gravity, until at last they cannot escape at all.

There is an ever-increasing delay in the time photons take to get to us, and while this is not time dilation, it is a redshift that looks just the same to us.

Mike

 

[Dale]

I'm just saying that there is only one process for calculating redshift. You don't have to do two calculations and add or multiply them together.

 

[PAllen]

I think this point was made earlier in this thread, but I would like to pose it in a graphic form. This is the point that an eternal black hole as described by SC geometry almost certainly does not exist in our universe. Let's instead look at formation of black hole.

To be able to see the formation better from afar, let's have the far fetched scenario of a trillion stars of some super cluster collapsing with no net angular momentum, no accretion disk forming. I pick the far fetched number of a trillion stars because that allows the black hole to form while the stars are still well separated from each other, and individually resolvable (in principle) up until the last moments. Let's further assume there is a background of galaxies behind this collapsing cluster, but nothing in your line of sight in front of it.

What would you see? As the collapse occurred, you would see the cluster, as a whole, reddening, and more and more extreme Einstein rings from galaxies behind the cluster. Up until the last moments, you would see highly red shifted light from stars throughout the cluster - especially, you could see stars in the center of the cluster. Then, in a relatively brief period of time, the cluster would further redden/darken until it was blacker than even CMB radiation. Against the background galaxies, it would look, quite literally, like a black hole in the sky surrounded by an Einstein ring of light from galaxies behind it.

How would you want to interpret this? It is a mathematical fact that this is what you would see. Would you say that a trillion stars have actually vanished? Would you say that the stars in center magically are compressed invisibly against the not quite yet formed horizon (having jumped billions of miles from the center of the cluster to the edge of this black ball)? You could say there is an invisible ball of a trillion frozen stars, a millimeter larger than the theoretical event horizon. Then, if matter falls in, it soon vanishes and the black region grows slightly (after all settles down). Again, you could say the black ball is still just larger than the theoretical event horizon, with frozen stars throughout, and new matter somewhere at the outer edge.

If you prefer this interpretation, it is, indeed, not determinable from outside observations that further collapse has occurred inside the black region. However, I would than ask:

If look like a duck, ... . Isn't black hole a good description of the this scenario? Then if you ask, what would happen according to a ship orbiting one of those interior stars? GR has only one answer - further collapse (to a singularity), in very finite time for the ship.

 

[Mike Holland]

OK, PAllen, that's a lovely scenario for me to go and think about. I am inclined towards the invisible ball of almost-frozen stars a millimeter larger than the EH, but need to get my mind around it. Maybe add some numbers to the scenario.
Mike

 

[Mike Holland]

Right, we have a very large, clumpy mass of gas collapsing. Most of the calculations using the Schwarzschild metric have been done for a gas of uniforn density, but I doubt that these trilllion tiny clumps in this massive cloud will affect the results. In what way do you think the clumps (stars) will make a difference to the calculations/simulations that have been done for collapsing clouds of gas?

"Up until the last moments, you would see highly red shifted light from stars throughout the cluster - especially, you could see stars in the center of the cluster. Then, in a relatively brief period of time, the cluster would further redden/darken until it was blacker than even CMB radiation."

I rather doubt that. We are talking about a Black Hole about 3x10**12 kilometers in radius (assuming sun-like stars) and weighing in at 2x10**45 grams. One kilometer from the horizon the time dilation would be 1,000,000:1, and a millimeter away it would be 1,000,000,000:1. The extreme reddening and weakening of the light would make it invisible long before it reached this stage.

In Newtonian terms, the volume of the BH would be 10**30 cubic kilometers, where the sun is 10**18 cubic kilometers. So the "clumps" could maintain their integrity as they pass through the EH, except that tidal forces might rip them apart, but all that is in their local timeframe.

I'm sticking with the calculations based on the Schwarzschild metric, a frozen ball of clumpy gas, but the clumps may stick out more than a millimeter!

Mike

 

[PAllen]

Right, we have a very large, clumpy mass of gas collapsing. Most of the calculations using the Schwarzschild metric have been done for a gas of uniforn density, but I doubt that these trilllion tiny clumps in this massive cloud will affect the results. In what way do you think the clumps (stars) will make a difference to the calculations/simulations that have been done for collapsing clouds of gas?

They don't. The purpose for the scenario is the idea of (in principle) seeing inside the collapsing cluster.

"Up until the last moments, you would see highly red shifted light from stars throughout the cluster - especially, you could see stars in the center of the cluster. Then, in a relatively brief period of time, the cluster would further redden/darken until it was blacker than even CMB radiation."

I rather doubt that. We are talking about a Black Hole about 3x10**12 kilometers in radius (assuming sun-like stars) and weighing in at 2x10**45 grams. One kilometer from the horizon the time dilation would be 1,000,000:1, and a millimeter away it would be 1,000,000,000:1. The extreme reddening and weakening of the light would make it invisible long before it reached this stage.

No disagreement with what I said. It is all a matter of what is meant by 'the last moments'. Millimeter was a figure of speech, not a calculation. Also, note that the 1 million factor of redshift would still be quite visible - you would be imaging gamma rays (of which there would be plenty) as light or radio waves. Only when the the highest energy gamma rays are shifted below the lowest detectable radio wave frequency would true invisibility occur. That would happen quite fast on astronomical time scale (but I have not calculate a specific number).

In Newtonian terms, the volume of the BH would be 10**30 cubic kilometers, where the sun is 10**18 cubic kilometers. So the "clumps" could maintain their integrity as they pass through the EH, except that tidal forces might rip them apart, but all that is in their local timeframe.

It is actually well known that for collapsing cluster this size (actually, a good bit smaller) tidal forces in the outer regions (but still well within the event horizon) are less than 1 g.

I'm sticking with the calculations based on the Schwarzschild metric, a frozen ball of clumpy gas, but the clumps may stick out more than a millimeter!

Mike

Agreed - not meant to be literal.

 

[PAllen]

Note, you have ignored the question of what GR predicts for a rocket orbiting a star in this cluster. It is one thing to say that you think this situation is one where GR breaks down. It is quite another to dispute that GR has a completely unambiguous prediction for the rocket inhabitants experience.

Note also, that the weight of evidence (IMO) is that the cosmic censorship hypothesis is false in GR; that is that naked singularities are a prediction of GR. First, sufficiently rapidly rotating collapse is shown to produce them in exact solutions (extreme parameters of the Kerr metric). Second, most numerical simulations of appropriate conditions indicate the formation (for a period of time) of naked singularities. See:

http://prd.aps.org/abstract/PRD/v19/i8/p2239_1

and a number of later studies reaching the same conclusion.

If naked singularities are predicted by GR it is completely untenable to claim that internal region of a collapsing cluster or cloud is not a real prediction of GR. You are in the absurd situation of claiming that if GR says an event horizon would form, it doesn't and the collapse doesn't proceed (just because one class of observer won't visually see it); while if an event horizon is not predicted, the collapse does proceed (because it can be seen), leading to the most extreme form of black hole - the naked singularity.

I suggest you adopt the consistent position (shared by a number of prominent physicists) that GR breaks down before formation of event horizons (let alone naked singularities) rather trying to dispute what GR predicts.

 

[Mike Holland]

Note, you have ignored the question of what GR predicts for a rocket orbiting a star in this cluster. It is one thing to say that you think this situation is one where GR breaks down. It is quite another to dispute that GR has a completely unambiguous prediction for the rocket inhabitants experience.

Good Lord! Have I expressed my views that badly? I don't believe GR breaks down anywhere. And as for the rocket inhabitants experience, I believe that GR has at least two equally valid and compatible predictions - from his point of view and from our point of view. In fact, I believe it covers all points of view. I have not gone into what happens inside an Event Horizon, because the maths is too complicated for me, and because I don't believe it is relevant to my argument which is all about what we see and infer about gravitational collapse, where Schwarzschild coords hold sway.

Note also, that the weight of evidence (IMO) is that the cosmic censorship hypothesis is false in GR; that is that naked singularities are a prediction of GR. First, sufficiently rapidly rotating collapse is shown to produce them in exact solutions (extreme parameters of the Kerr metric). Second, most numerical simulations of appropriate conditions indicate the formation (for a period of time) of naked singularities. See:

http://prd.aps.org/abstract/PRD/v19/i8/p2239_1

and a number of later studies reaching the same conclusion.

OK, I was not aware of these calculations, and need to do some studying. But the main issue for my topic will be - How long does it take for such a singularity to form, from our external point of view. If they form in a finite time, then I guess my whole argument collapses.

If naked singularities are predicted by GR it is completely untenable to claim that internal region of a collapsing cluster or cloud is not a real prediction of GR. You are in the absurd situation of claiming that if GR says an event horizon would form, it doesn't and the collapse doesn't proceed (just because one class of observer won't visually see it); while if an event horizon is not predicted, the collapse does proceed (because it can be seen), leading to the most extreme form of black hole - the naked singularity.

Now you are mis-representing me. All along I have followed the predictions of GR, that a collapsing supermassive star (or whatever) would, in its own timeframe, form an Event Horizon and then collapse to a singularity. I have never denied this. But I have also quoted and agreed with a number of experts who calculate that this collapse to a Black Hole will take an infinite time in our remote observer timeframe.

You are taking the untenable position of claiming that only one timeframe is valid for describing these events - the local one. We don't visually see it because it hasn't happened in our time frame. The collapse proceeds in both timeframes - at different rates. Slower and slower in ours, and very swiftly in the local one. If you can't get your head around time flowing differently from different points of view (and time frames) and both points of view being equally valid, then you will never grasp this.

I can understand that some cosmologists would think GR breakls down at the EH, because the maths disagrees with their belief that Black Holes exist. I am convinced that GR is valid all the way.

Thanks for the info about naked singlarities.

Mike

 

[PAllen]

Good Lord! Have I expressed my views that badly? I don't believe GR breaks down anywhere. And as for the rocket inhabitants experience, I believe that GR has at least two equally valid and compatible predictions - from his point of view and from our point of view. In fact, I believe it covers all points of view. I have not gone into what happens inside an Event Horizon, because the maths is too complicated for me, and because I don't believe it is relevant to my argument which is all about what we see and infer about gravitational collapse, where Schwarzschild coords hold sway.

SC coordinates are just one choice for external observers. Claiming they are the only valid choice for external observers violates the essence of GR - that coordinates are purely a matter of convention, for all observers. It is equally valid for external observers to use any other coordinates.

Consider this phrase: "what we see and infer about gravitational collapse". You insist, actually, that we are not allowed to infer anything we don't see. That is an absurd restriction, throughout physics.

I haven't seen your answer to the difference between 'see' and infer for the following simple SR prediction, that I and several others have raised:

- two rockets accelerate away from each other at 1g. Quickly, each can not see or send signals to each other or to much of the universe. Each may continue to infer about the other rocket or the invisible universe. They are not required to consider that what they don't see doesn't exist for them.

OK, I was not aware of these calculations, and need to do some studying. But the main issue for my topic will be - How long does it take for such a singularity to form, from our external point of view. If they form in a finite time, then I guess my whole argument collapses.

Definitely finite time as seen by external observer. Also, note my wording versus yours:

As seen by some observer = as happens according to some observer

is a misinterpretation of GR. Consider yet again the acceleration rocket examples.

Now you are mis-representing me. All along I have followed the predictions of GR, that a collapsing supermassive star (or whatever) would, in its own timeframe, form an Event Horizon and then collapse to a singularity. I have never denied this. But I have also quoted and agreed with a number of experts who calculate that this collapse to a Black Hole will take an infinite time in our remote observer timeframe.

You have misinterpreted them as shown by examining their quotes in context (in most cases), and especially by looking at scientific writings versus popular writings. There are no global frames in GR. There are local frames and global coordinates. The former represent physics, the latter are matters of convention. The predicitions of GR about a 'universe' include all the coordinate charts (each arbitrary) needed to cover the universe.

You are taking the untenable position of claiming that only one timeframe is valid for describing these events - the local one. We don't visually see it because it hasn't happened in our time frame. The collapse proceeds in both timeframes - at different rates. Slower and slower in ours, and very swiftly in the local one. If you can't get your head around time flowing differently from different points of view (and time frames) and both points of view being equally valid, then you will never grasp this.

Obviously, I think it is you who is taking the untenable position. What we see and what we may conclude happens are different, throughout physics. Note that in addition to saying a distant observer sees clocks approaching an event horizon slow down and stop relative to theirs, it also says the infalling observer sees our clocks proceeding normally (not at the same rate, but differing only by a finite factor) compared to theirs, through the event horizon and up to the singularity. So which is the real time rate comparison between external in infalling observers? GR really says there is no unique answer to to this question, not that an external observer must interpret the comparison using SC coordinates.

I can understand that some cosmologists would think GR breakls down at the EH, because the maths disagrees with their belief that Black Holes exist. I am convinced that GR is valid all the way.

Thanks for the info about naked singlarities.

Mike

Just to be clear, if you think GR is valid all the way, then doesn't that include the validity of what the rocket in my collapsing cluster experiences?

What almost all physicists think is that when quantum effects are taken into account, singularities do not actually form, in contradiction to GR predictions [Even you agree GR predicts a singularity for the rocket observer in my collapse scenario]. As for event horizons, there are a wider range of views about what a quantum corrections to GR would imply, and the issues flow from ideas about Hawking radiation and quantum information. Some think you get something that looks macroscopically like a horizon, but microscopically it is not; some think you get nothing resembling a horizon; and many other variations as well.

 

[TrickyDicky]

What almost all physicists think is that when quantum effects are taken into account, singularities do not actually form, in contradiction to GR .

Are you sure? I don't have any reliable way to confirm that about physicists in general, but I don't think physicists here at PF think that.
In any case if what you say is true, that would mean BH's are no longer mainstream objects in physics.

 

[PAllen]

Are you sure? I don't have any reliable way to confirm that about physicists in general, but I don't think physicists here at PF think that.
In any case if what you say is true, that would mean BH's are no longer mainstream objects in physics.

I've seen almost all experts here at PF who have expressed an opinion state:

- singularities are predicted by GR
- singularities almost certainly don't actually exist, and this prediction shows GR breaks down in these extreme regions.

I have seen the same thing in my reading of professional papers.

However, your conclusion doesn't follow. Most professional physicists I know of, definitely believe BH's are part of our universe and are mainstream physics. They would have many of the macroscopic properties predicted by GR, but differ in details. Among those differences is that there is no actual singularity at the 'center'. As I mentioned, there is a wider range of views about the likely 'real nature' of the horizon. I think (this is more of guess compared to singularity viewpoint) is that a majority think the efforts to visualize a horizon in galactic center BH's will come out positive. This simply means there is something macroscopically behaves a lot like a horizon. There are several speculative theories of BSM physics that have this feature macroscopic horizon-like behavior, while micrcoscopically, there is no horizon.

[Edit: Let me reverse the challenge: I can think of no physicist in history who has stated they believe the GR prediction of actual singularities is true of reality, rather than an indication of breakdown of GR.]

 

[TrickyDicky]

I've seen almost all experts here at PF who have expressed an opinion state:

- singularities are predicted by GR
- singularities almost certainly don't actually exist, and this prediction shows GR breaks down in these extreme regions.

I have seen the same thing in my reading of professional papers.

However, your conclusion doesn't follow. Most professional physicists I know of, definitely believe BH's are part of our universe and are mainstream physics. They would have many of the macroscopic properties predicted by GR, but differ in details. Among those differences is that there is no actual singularity at the 'center'. As I mentioned, there is a wider range of views about the likely 'real nature' of the horizon. I think (this is more of guess compared to singularity viewpoint) is that a majority think the efforts to visualize a horizon in galactic center BH's will come out positive. This simply means there is something macroscopically behaves a lot like a horizon. There are several speculative theories of BSM physics that have this feature macroscopic horizon-like behavior, while micrcoscopically, there is no horizon.

I wouldn't consider the singularity in a black hole a mere "detail" one can simply drop. Without singularity there is no theoretical justification for the black hole concept, you may have some other object or process that explains certain astrophysical observations but certainly wouldn't be a BH unless one defines it as "whatever there is up there that was formerly known and interpreted as a black hole".

 

[PAllen]

I wouldn't consider the singularity in a black hole a mere "detail" one can simply drop. Without singularity there is no theoretical justification for the black hole concept, you may have some other object or process that explains certain astrophysical observations but certainly wouldn't be a BH unless one defines it as "whatever there is up there that was formerly known and interpreted as a black hole".

The absence of the singularity is not detail - it is a signal of breakdown of GR. What differs only in possibly undetectable detail is the properties of an actual BH (modified by quantum corrections with no singularity), versus a classical GR black hole with a singularity as observed from afar.