# Black Holes - the two points of view.

1. Aug 10, 2012

### 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 in to 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

2. Aug 10, 2012

### pervect

Staff Emeritus
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 simlar 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".

3. Aug 10, 2012

### 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

Last edited: Aug 10, 2012
4. Aug 10, 2012

### 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

5. Aug 10, 2012

### Staff: Mentor

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.

6. Aug 10, 2012

### Staff: Mentor

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.

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 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:

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

7. Aug 10, 2012

### Staff: Mentor

8. Aug 10, 2012

### Naty1

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

Dalespam posts:

9. Aug 10, 2012

### Naty1

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 apparant 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.

10. Aug 10, 2012

### pervect

Staff Emeritus
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 [Broken] has the formulae, converting them to latex they are:

$$t = \frac{c}{a} sinh \frac{aT}{c} = \sqrt{ \left(\frac{d}{c}\right) ^2 + \frac{2d}{a} }$$
$$d = \frac{c^2}{a} \left( cosh \frac{aT}{c} - 1\right) = \frac{c^2}{a} \sqrt{1 + \left(\frac{aT}{c}\right)^2 - 1}$$

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.

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.

Last edited by a moderator: May 6, 2017
11. Aug 10, 2012

### DrGreg

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.

12. Aug 10, 2012

### pervect

Staff Emeritus
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.

13. Aug 10, 2012

### DrGreg

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.

14. Aug 11, 2012

### 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

15. Aug 11, 2012

### 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.

16. Aug 11, 2012

### Staff: Mentor

As far as I know, the quotes you refered 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.

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".

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

17. Aug 11, 2012

### Staff: Mentor

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 Schwarzchild 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.

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

18. Aug 11, 2012

### 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.

19. Aug 11, 2012

### 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
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.

20. Aug 11, 2012

### 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/Eddington-Finkelstein_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.

Last edited: Aug 11, 2012