Can Black Holes Truly 'Grow' in the Lifetime of the Universe?

[A.T.]

- An observer riding with collapsing matter
- An observer remaining outside

Is it possible to present a smooth transition between those two cases?

Consider an infinite number of observers, all simultaneously starting at the same point outside the BH, but undergoing different proper accelerations ranging from a=0 (free fall into the BH) to a=a_hover (allows keeping r=const). How would the free falling one be observed by the others? Which ones would see him cross the EH and after which time on their clocks?

 

[PAllen]

Is it possible to present a smooth transition between those two cases?

Consider an infinite number of observers, all simultaneously starting at the same point outside the BH, but undergoing different proper accelerations ranging from a=0 (free fall into the BH) to a=a_hover (allows keeping r=const). How would the free falling one be observed by the others? Which ones would see him cross the EH and after which time on their clocks?

As long as an observer remains outside the EH, they will not see any object cross the EH. If they stop madly accelerating (it takes asymptotically infinite acceleration as measured by an accelerometer to avoid crossing the EH as you get close to it; and this, by the way, is trivial for a distant observer to compute using only external SC coordinates) and fall through the EH, they will see prior infallers as of when they crossed the EH.

The behavior is very similar to a uniformly accelerating rocket and its Rindler horizon. If the rocket drops a series of probes, it will see them freeze, one after the other at its Rindler horizon (this is all SR). Only if it stops accelerating, so that the Rindler horizon overtakes it, will it see these dropped probes crossing the horizon, and see their subsequent history.

 

[DrGreg]

How would the free falling one be observed by the others? Which ones would see him cross the EH and after which time on their clocks?

There is only one way for you to visually observe something crossing a perpetual event horizon, and that is for you to cross the horizon yourself. That moment is precisely when you will see it, as the horizon itself is a wavefront of light traveling away from the hole. But there's no flagpole to mark the location of the horizon so you wouldn't notice it had happened; you'd see the other object moving continuously from outside to inside the horizon.

Anyone moving radially with insufficient constant proper acceleration to hover will fall through the horizon in finite proper time (at which moment they'll see falling through anyone else who fell through before them).

 

[DrGreg]

For a distant observer, he must conclude an EH never forms, by his clock, in finite time.

The problem is that you can only use your own clock to measure things that happen right next to you. To measure things a distance away from you, you have to invent a definition of simultaneity and maybe use someone else's clock that has been synchronised using your definition. Some events may lie outside the region you have chosen to apply your definition. Does this mean those events don't exist?

Consider the following example from special relativity. A ("Born rigid") rocket has constant proper acceleration in empty space, far from any gravity. At any instant in time, you can define distance and simultaneity according to an inertial observer who is momentarily at rest relative to the rocket. You can "glue" all these observers together to form a valid coordinate system ("Rindler coordinates") for the rocket. Here's a spacetime diagram showing the distance X and time T of an inertial frame, and the pink grid lines show the rocket's Rindler coordinates x and t. The curved line x=1 represents one point on the rocket.

Dr Greg, Wikimedia Commons, CC BY-SA 3.0

The white area above this chart is not covered by the pink grid. Even after waiting an infinite time t, none of the events in that area become simultaneous with an event on the rocket as measured by the rocket. Yet these events do have a finite inertial T coordinate. Would you say that the events in those areas "do not exist"?

 

[arindamsinha]

The problem is that you can only use your own clock to measure things that happen right next to you. To measure things a distance away from you, you have to invent a definition of simultaneity and maybe use someone else's clock that has been synchronised using your definition. Some events may lie outside the region you have chosen to apply your definition. Does this mean those events don't exist?...

...none of the events in that area become simultaneous with an event on the rocket as measured by the rocket. Yet these events do have a finite inertial T coordinate. Would you say that the events in those areas "do not exist"?

You have outlined the situation quite well. Then the question is, when, by our own clock, does the event happen?

I feel the event I am talking about (matter crossing EH) is always in the future, getting asymptotically closer to the EH, but never reaching it. Yes, by our own clock, and my question is based on our own clock (can black hole EH grow for external observers?).

I understand that the event may actually happen for an observer falling into the black hole, but by our clock, this falling observer also never reaches the event horizon! So I stand by the statement that the event "does not exist" or come to pass ever, by our clock.

This is where I see a conflict. From our point of view, drawing a geometric parallel, two lines are asymptotic and only meet at infinity, and never cross over. For the observer falling into the BH, not only do the two lines meet, but they even cross over.

I am getting the feeling that there is still some lack of appropriate interpretation of GR in this area, or perhaps, GR may have to be further generalized in this area for a proper interpretation of Universal events (If we accept the astronomical conclusion that black holes exist, and grow in finite time of external observers' clocks).

That is, unless we accept the other possible explanation that black holes never really fully form, but get aymptotically closer to forming all the time.

 

[PeterDonis]

I understand that the event may actually happen for an observer falling into the black hole, but by our clock, this falling observer also never reaches the event horizon! So I stand by the statement that the event "does not exist" or come to pass ever, by our clock.

You can look at it this way, as long as you only draw valid conclusions from your statement. For example, it is valid to conclude that events at or inside the event horizon can never causally affect you (because no causal influence can travel faster than light), so in that sense you can behave as if they don't "exist". But it isn't valid to conclude that *nobody* can ever feel any causal influence from those events, because someone could always choose to fall into the black hole.

This is where I see a conflict. From our point of view, drawing a geometric parallel, two lines are asymptotic and only meet at infinity, and never cross over.

You have to be careful interpreting what "only meet at infinity" means. You appear to be picturing it the way it would work on a flat Euclidean plane: two parallel lines on a plane "only meet at infinity", meaning that you can extend them to any finite length you like and they will never meet.

This is *not* true for the worldlines of two infalling objects that meet inside the horizon. "Length" along worldlines in spacetime means proper time, and the two objects will meet in a *finite* amount of proper time. You already agree with this, but you apparently haven't fully comprehended what it means. It means that the two lines are *not* "infinitely long" before they meet below the horizon, in the way that parallel lines on a Euclidean plane are "infinitely long" before they meet. You can only extend the two worldlines for a finite length before they meet, even though doing so covers an infinite range of the distant observer's time coordinate.

In other words, when you have extended the two lines "to infinity" according to your clock, you have only extended them to a finite length in geometrically invariant terms. You have chosen a time coordinate that is so distorted at the horizon that it extends finite lengths (i.e., finite proper times) so they look like infinite lines. The analogy you are trying to draw with "infinite lines" in ordinary plane geometry does not work; the lines that "look infinite" to the distant observer because of his choice of time coordinate are *not infinite*.

I am getting the feeling that there is still some lack of appropriate interpretation of GR in this area

No, it is just that you don't fully understand what the standard GR picture says. The above may help.

That is, unless we accept the other possible explanation that black holes never really fully form, but get aymptotically closer to forming all the time.

No, this "explanation" does not work; it amounts to claiming that the lines that "look infinite" in your time coordinate really are infinite, in the way parallel lines on the Euclidean plane are infinite. That is not correct. See above.

 

[arindamsinha]

PeterDonis, let me first acknowledge that I have learned a lot in this forum from many members, and you have been especially helpful across multiple threads in clearing up many of my doubts and misconceptions patiently. The responses I am making below is not just to be stubborn, but because I genuinely believe I am not getting a satisfactory explanation that I can accept, yet.

You can look at it this way, as long as you only draw valid conclusions from your statement... But it isn't valid to conclude that *nobody* can ever feel any causal influence from those events...

We are on the same page. I have repeatedly mentioned that I am being partial to the external observer's point of view in this thread.

You have to be careful interpreting what "only meet at infinity" means. You appear to be picturing it the way it would work on a flat Euclidean plane: two parallel lines on a plane "only meet at infinity", meaning that you can extend them to any finite length you like and they will never meet.

This is *not* true for the worldlines of two infalling objects that meet inside the horizon. "Length" along worldlines in spacetime means proper time, and the two objects will meet in a *finite* amount of proper time. You already agree with this, but you apparently haven't fully comprehended what it means. It means that the two lines are *not* "infinitely long" before they meet below the horizon, in the way that parallel lines on a Euclidean plane are "infinitely long" before they meet. You can only extend the two worldlines for a finite length before they meet, even though doing so covers an infinite range of the distant observer's time coordinate.

In other words, when you have extended the two lines "to infinity" according to your clock, you have only extended them to a finite length in geometrically invariant terms. You have chosen a time coordinate that is so distorted at the horizon that it extends finite lengths (i.e., finite proper times) so they look like infinite lines. The analogy you are trying to draw with "infinite lines" in ordinary plane geometry does not work; the lines that "look infinite" to the distant observer because of his choice of time coordinate are *not infinite*.

I was not thinking about parallel lines (e.g. y = 0 and y = 1) which only technically meet at infinity. I was referring to something like y = 0 and y = 1/x, which do not meet in finite axes, but the distance keeps getting shorter with increasing x. There is a distinction here that I would like to draw your attention to.

Hope that clarifies what I meant, again from the external observer's point of view.

From the in falling observer's point of view, this may be something like y = 0 and y = 1/x - 1.

Don't take the equations literally... I am not trying to say that these in any way follow from or are related to GR equations... just trying to illustrate what I meant.

No, it is just that you don't fully understand what the standard GR picture says. The above may help.

I think it is an unwarranted conclusion to state that there is a single accepted 'standard GR picture'. Even in this thread we have seen at least two methods of interpreting these phenomena in terms of GR, and they are not totally compatible. There may even be a majority view interpretation, but the other views are also advanced by credible scientists and should not be just dumped as wrong. Science is often a democracy, but many advances have come from the minority view (e.g. Galileo's and Einstein's points of view before they were accepted as *correct*)

No, this "explanation" does not work; it amounts to claiming that the lines that "look infinite" in your time coordinate really are infinite, in the way parallel lines on the Euclidean plane are infinite. That is not correct. See above.

This I cannot agree to. Why can't it be true that black holes are always in the method of formation, but never fully form? That would nicely explain a lot of things that we find weird. Why can't the O-S model in its original form, which you were kind enough to explain to me, be correct? I am not claiming that it is necessarily correct, but something to think about.

Must we assume that what are observed to be black holes in the Universe must necessarily be Schwarzschild black holes and a 'fait accompli', and not something eternally in formation? The latter would probably show the same behaviour as completely formed black holes, at the distances from which we are looking?

 

[PAllen]

I feel the event I am talking about (matter crossing EH) is always in the future, getting asymptotically closer to the EH, but never reaching it. Yes, by our own clock, and my question is based on our own clock (can black hole EH grow for external observers?).

And this remains the nub of the matter. There is no ambiguity about what an external observer sees, detects, or an accelerating rocket sees or detects. But as soon as you talk about what happens 'over there' by my clock, we are in the realm of arbitrary convention, not physics. Routinely, for distant observations, we correct for light travel time. If light travel time is very slow, we might want to heavily adjust. Among other things:

- we can compute what happens 'over there' that we cannot see. Why on Earth would we expect that what any observer sees defines what exists?
- we could, if we want, adopt a simultaneity convention that attaches a time per our clock to events inside the event horizon. I have shown one way to do this in #23 of this thread. This is one way of adjusting for slow light travel time.

 

[PAllen]

You have outlined the situation quite well. Then the question is, when, by our own clock, does the event happen?

And the answer is, any time we want such that there is a spacelike connection between the time we pick on our world line and the distant event. This is the only physical restriction. All else is convention. SC coordinates (for BH) and Rindler coordinates for rocket, pick 'never'. My #23 proposal for BH, and something equivalent for rocket, pick finite times for events that cannot be visually observed.

 

[PeterDonis]

PeterDonis, let me first acknowledge that I have learned a lot in this forum from many members, and you have been especially helpful across multiple threads in clearing up many of my doubts and misconceptions patiently.

Thanks!

The responses I am making below is not just to be stubborn, but because I genuinely believe I am not getting a satisfactory explanation that I can accept, yet.

No problem. I don't expect you, or anyone, to accept what I say without really understanding and agreeing with it.

I was not thinking about parallel lines (e.g. y = 0 and y = 1) which only technically meet at infinity. I was referring to something like y = 0 and y = 1/x, which do not meet in finite axes, but the distance keeps getting shorter with increasing x. There is a distinction here that I would like to draw your attention to.

I see the distinction, but it's irrelevant here. The point is that the worldlines of infalling observers, when you extend to t = infinity (t is the Schwarzschild time coordinate), have a *finite length*. That means this case is *different* from the case of lines y = 0 and y = 1/x, where x goes to infinity; the lengths of those lines increase without bound as x goes to infinity. The lengths of worldlines falling to the horizon do *not* increase without bound as t goes to infinity.

From the in falling observer's point of view, this may be something like y = 0 and y = 1/x - 1.

It isn't. See above.

I think it is an unwarranted conclusion to state that there is a single accepted 'standard GR picture'.

There is about the fact that the lengths (proper times) of infalling worldlines are finite as t goes to infinity. That is easy to prove mathematically using the GR equations; physics students are routinely asked to do so as a homework problem. There may be aspects of GR that are open to "interpretation", but this is not one of them. What I'm saying on this particular topic has been "a single accepted standard GR picture" since the 1960's.

This I cannot agree to. Why can't it be true that black holes are always in the method of formation, but never fully form?

Because the proper time experienced by an infalling observer to reach the horizon is finite. The spacetime curvature at the horizon is finite. And outgoing light at the horizon stays at the horizon. Those three facts, combined, show that there *must* be a region of spacetime on the other side of the horizon, even if it can't be seen by a distant observer.

However, this is partly a matter of words. If one interprets "never fully form" to mean only "never fully form in the region of spacetime covered by finite values of the Schwarzschild time coordinate", then it *is* true that black holes "never fully form" in this restricted sense. But if you mean "never fully form" in any stronger sense than that, then the statement is *not* true; BH's *do* "fully form" when you look at the entire spacetime. It's just that the entire spacetime can't be covered by the standard SC time coordinate.

Many pop-science books and articles about relativity, and even some textbooks and physics papers, use language like "never fully form" in the restricted sense, sometimes without fully realizing it. This causes a lot of confusion and argument when people read the books or articles and interpret the language in the strong sense. This is one reason why physicists don't use English, or any other natural language, as their primary medium for expressing and communicating theories; they use math, which has a precision that natural language does not.

That would nicely explain a lot of things that we find weird. Why can't the O-S model in its original form, which you were kind enough to explain to me, be correct?

It is correct. The original O-S model simply did not address the question of what happens *after* a collapsing object forms a horizon. Their original paper doesn't talk about that at all; they show that the proper time experienced by an observer riding on the surface of the collapsing star is finite at the instant the horizon forms; and they show that the Schwarzschild coordinate time taken for this to happen is infinite. All of this is correct. But then they stop; they go no further. Their model is correct, but it's also incomplete.

Must we assume that what are observed to be black holes in the Universe must necessarily be Schwarzschild black holes and a 'fait accompli', and not something eternally in formation?

In so far as there is a difference between a "real black hole" and "something eternally in formation", the answer I would give is yes. See above for comments about the use of language here.

 

[arindamsinha]

And this remains the nub of the matter. There is no ambiguity about what an external observer sees, detects, or an accelerating rocket sees or detects. But as soon as you talk about what happens 'over there' ...

My intention in this topic had been to somehow relate the 'my clock' and 'over there' scenarios. Perhaps that may not be really possible, but thanks for all the responses.

And the answer is, any time we want such that there is a spacelike connection between the time we pick on our world line and the distant event. This is the only physical restriction. All else is convention. SC coordinates (for BH) and Rindler coordinates for rocket, pick 'never'. My #23 proposal for BH, and something equivalent for rocket, pick finite times for events that cannot be visually observed.

Source of thoughts for my starting this topic - is it not really possible to explain all physical phenomena in terms of a consistent view from an observer outside and far from black holes? Perhaps it is not possible... I am willing to let that answer ride for the time being, and pick up more specific points later in other topics...

The point is that the worldlines of infalling observers... the fact that the lengths (proper times) of infalling worldlines are finite as t goes to infinity... There may be aspects of GR that are open to "interpretation", but this is not one of them... the proper time experienced by an infalling observer to reach the horizon is finite...


The original O-S model simply did not address the question of what happens *after* a collapsing object forms a horizon... they go no further... In so far as there is a difference between a "real black hole" and "something eternally in formation", the answer I would give is yes...

Thanks for your detailed responses. I will think about this, and some of it may be material for a future topic. I was trying to look at this phenomenon from the point of view of external observers only. The in-falling observer keeps cropping up, perhaps because there cannot be an explanation purely from the point of view of the external observer where relativity is concerned...

Nevertheless, I have gained some valuable insights, and am good to go with this for a little while...

 

[PAllen]

My intention in this topic had been to somehow relate the 'my clock' and 'over there' scenarios. Perhaps that may not be really possible, but thanks for all the responses.

Congratulations! If you think further on this you are well on the way to understanding both SR and GR - both of which emphatically say there is no absolute, unique, or even preferred way to do this except nearby.

 

[harrylin]

[..] Is that what the 'O-S model' states? What is the 'OS-model', in brief, to explain to a layman like me?

I had forgotten to comment on that. In a recent thread I cited some for this topic essential parts:
https://www.physicsforums.com/showpost.php?p=4162425&postcount=50

As you see, their model has apart of Dopper shift a gravitational red-shift, (1-r_o/r_b)^½ and to a distant observer the [infalling] motion will be slowed up by a factor (1-r_o/r_b). They state there that it is impossible for a singularity to develop in a finite time. However, they next consider a proper time after infinite time t. Perhaps they had not completely thought it through; Einstein's paper on that same topic was published after they submitted their paper.

 

[PeterDonis]

They state there that it is impossible for a singularity to develop in a finite time.

By which they mean a finite time according to a clock at r = infinity, i.e., a finite Schwarzschild coordinate time. As you note next, and as I noted in my previous post, they also show that the proper time experienced by an observer riding on the surface of the collapsing matter, at the point where the collapsing matter forms a horizon, is finite.

Perhaps they had not completely thought it through

As I said in my last post, it looks to me like they simply left their model incomplete; they did not even address in their paper the question of whether or not there was any region of spacetime beyond the horizon. They simply stop their analysis at the point where the horizon forms.

Einstein's paper on that same topic was published after they submitted their paper.

Actually, Einstein's paper was considering a different scenario; Einstein was considering the case of a stationary configuration of masses, i.e., a configuration of masses whose metric does not change with time. Matter which is collapsing, as in the O-S model, is not stationary, and is not what Einstein was considering.

 

[harrylin]

By which they mean a finite time according to a clock at r = infinity, i.e., a finite Schwarzschild coordinate time. As you note next, and as I noted in my previous post, they also show that the proper time experienced by an observer riding on the surface of the collapsing matter, at the point where the collapsing matter forms a horizon, is finite.

Yes of course. It sounds as if you want to say something with that, but it never comes out. It goes a bit like this:
A: Macy has a black bag, just as Dick thought.
B: But Anne has a brown bag.

[..] They simply stop their analysis at the point where the horizon forms.

Not exactly: as I cited, although they don't literally state it, they talk about t>∞. That doesn't make sense to me, which is what I had in mind with my remark that it looks like they didn't fully think it through. And that's not so strange, as their results were new.

Actually, Einstein's paper was considering a different scenario; Einstein was considering the case of a stationary configuration of masses, i.e., a configuration of masses whose metric does not change with time. Matter which is collapsing, as in the O-S model, is not stationary, and is not what Einstein was considering.

Almost so: "it does not seem to be subject to reasonable doubt that more general cases will have analogous results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light".
And what I meant: his paper (and in particular its conclusion) would have incited them to reflect on and discuss what actually will happen according to their model.

 

[EskWIRED]

The observer outside always 'sees' a very near black hole, with an 'almost horizon' (note, this 'almost horizon' is blacker than anything else in the universe in finite time for the external observer - however, technically, it has not quite become a horizon as seen by the outside observer. When more matter falls in, the outside obsever sees the 'almost horizon' grow. So everything is always an 'almost black hole' as seen by an outside observer.

However, you can't call it relativity an claim there is only one allowed type of observer. Further, as with all cases of getting light, you make deductions about what has happened where the light was emitted, since it was emitted. If you ask these question, you have no choice but to consider there is a black hole horizon and singularity, and new matter falls through the horizon and reaches the singularity in finite time. GR tells you that the light you see coming from a collapsed object is exceedingly ancient light - so you ask what happened since it was emitted, for the object itself. GR has only one answer to this - if became a singularity, even though you will never see this.

I think that I understand everything written above. I also understand that it would be impossible to see an even horizon with a telescope, given that it is black and given that it is likely surrounded by infalling matter.

But what I don't understand is whether we "see" all areas containing black holes as the same size in our images of them, or whether the size of different black holes "appears" to vary.

Do we infer the different sizes of black holes based upon phenomenon other than how much of the sky they blot out? For example, do we infer the size based solely upon the effects observed outside the EH, such as the velocity of orbiting matter? Or do we measure anything by how much of the background is blotted out by the apparent width of the event horizon?

 

[PeterDonis]

Yes of course. It sounds as if you want to say something with that, but it never comes out. It goes a bit like this:
A: Macy has a black bag, just as Dick thought.
B: But Anne has a brown bag.

To me it goes more like this:

A. Macy has a black bag, just as Dick thought. That means there can never be any brown bags anywhere.
B. But Anne has a brown bag.

Not exactly: as I cited, although they don't literally state it, they talk about t>∞. That doesn't make sense to me, which is what I had in mind with my remark that it looks like they didn't fully think it through.

I think they didn't fully explore the question of what the region of spacetime with "t > infinity" would look like. But just contemplating the existence of such a region is not a contradiction. Check my latest post in the simultaneity thread.

Almost so: "it does not seem to be subject to reasonable doubt that more general cases will have analogous results. The "Schwarzschild singularity" does not appear for the reason that matter cannot be concentrated arbitrarily. And this is due to the fact that otherwise the constituting particles would reach the velocity of light".

It depends on what kinds of "more general cases" he was thinking about. Reading his paper, it looks to me like the assumption of a stationary system is crucial; if it is dropped his conclusions no longer hold. So his analysis *would* apply to systems like neutron stars, even if they weren't completely symmetric, and I believe it does; his analysis basically says that *any* system that is in a stable equilibrium has to have a radius of at least 9/8 the Schwarzschild radius for its mass. But a collapsing star such as O-S modeled is not in a stable equilibrium; I don't see any indication from the paper that Einstein really considered that case, but of course I may be wrong.

And what I meant: his paper (and in particular its conclusion) would have incited them to reflect on and discuss what actually will happen according to their model.

I agree this is certainly possible; even if Einstein didn't consider the non-equilibrium case, it's likely that O-S would have made the connection. They wouldn't have had a lot of time, though; the O-S paper was published on September 1, 1939 (the day Germany invaded Poland and started World War II).

 

[harrylin]

To me it goes more like this:

A. Macy has a black bag, just as Dick thought. That means there can never be any brown bags anywhere.
B. But Anne has a brown bag.

I now understand the misunderstanding (which has lasted for weeks) but not the cause. For what happened was the following, with in brackets what people thought:

A: (I see that everyone agrees that Anne has a brown bag. That is fine to me, even Macy says that Anne has a brown bag. Dick says that he thinks that Macy has a black bag, but that he had never heard anyone say so. However I have seen this actually been said and explained, and it solves the puzzle for me. But for some reason this is not taken seriously)
A: Macy has a black bag, just as Dick thought.
B: (A misrepresents the situation by saying that Macy has a black bag, for he means that there can never be any brown bags anywhere)
B: But Anne has a brown bag.

As this is also coming up in the other thread, we will surely discuss it in detail there, when time permits.

[..] It depends on what kinds of "more general cases" he was thinking about. [..]

According to some people here Einstein's conclusion was wrong; probably they interpret his conclusion the way I do. I still hope to see the paper that is claimed to have proved it wrong.

 

[PeterDonis]

According to some people here Einstein's conclusion was wrong; probably they interpret his conclusion the way I do.

It depends on which "conclusion" you refer to. AFAIK his conclusion that a system *in stable equilibrium* can never have a radius less than 9/8 the Schwarzschild radius for its mass is correct, and is considered to be correct by mainstream classical GR. However, his claim that this means *no* system can collapse inside that radius and form a horizon (and later on, a curvature singularity at r = 0, at least in the classical case) is *not* correct, because his analysis doesn't apply to systems that are not in stable equilibrium, and systems undergoing gravitational collapse are not in stable equilibrium; AFAIK this is also part of mainstream classical GR.

I still hope to see the paper that is claimed to have proved it wrong.

I'm not familiar enough with the literature to know if anyone ever specifically responded to Einstein's paper. However, the statements I made above are based on my understanding of current mainstream classical GR in general, not specifically concerned with Einstein's paper and its claims. I believe MTW, at least, specifically talk about static equilibrium only being possible for radius > 9/8 of the Schwarzschild radius, and how a collapsing system is not in static equilibrium and so is not subject to that limitation on radius. I can't remember if they reference Einstein's paper; when I get a chance I'll dig into my copy to see.

 

[PAllen]

I think that I understand everything written above. I also understand that it would be impossible to see an even horizon with a telescope, given that it is black and given that it is likely surrounded by infalling matter.

But what I don't understand is whether we "see" all areas containing black holes as the same size in our images of them, or whether the size of different black holes "appears" to vary.

Do we infer the different sizes of black holes based upon phenomenon other than how much of the sky they blot out? For example, do we infer the size based solely upon the effects observed outside the EH, such as the velocity of orbiting matter? Or do we measure anything by how much of the background is blotted out by the apparent width of the event horizon?

The size of black hole is determine by its mass. Currently, evidence for things 'very much like BH' is strong but indirect, and the distinctions between objects are mass. This is determined by the motion of nearby stars.

However, within the next decade, it is expected that we will succeed in directly imaging the apparent horizon of the BH in our galaxy and also in some nearby galaxies (M87 is often mentioned). These observations should be enough to verify or falsify one specific quantum gravity prediction:

There is a small group of quantum gravity theorists (Baryshev, et. al.) that propose nothing at all exists where GR predicts the event horizon. Instead collapse stops about 2/3 of this radius. Upcoming observations should be sufficient to confirm or reject this prediction. (Most expect it will be rejected). But it is a rare, specific, falsifiable quantum gravity prediction, and that is a good thing.

 

[thehangedman]

The event horizon is a place where the metric tensor contains an infinity. Thus, there are no null geodesics (light paths) that cross this "line". This gets quite sticky, as infinities pose a whole host of mathematical problems that most physicists just choose to ignore (not all). I am of the opinion that any final theory that integrates quantum mechanics will resolve this issue. There is likely a form of quantum tunneling that occurs once particles get close enough to the event horizon that allows them to make their way in (an, in essence, out) of the black hole in a finite time as observed from us on the outside.

That said, if you stick strictly to only GR, the outside observer will never "see" the particle cross the event horizon. Information, in all forms, cannot escape from the inside of the BH, be it light or any other effect. Like other people have noted however, the total gravity experienced by the outside observer changes immediately after the particle falls between the observer and the BH anyway. Thus, the only information an outside observer could actually "see" happened long before the particle gets to the event horizon.

 

[PAllen]

The event horizon is a place where the metric tensor contains an infinity.

False. It is a place where this happens in one coordinate system that is ill fitted to this region. In other coordinates this does not happen. On the other hand, even these coordinates you can show that curvature is finite at the EH.

Thus, there are no null geodesics (light paths) that cross this "line".

False again. There are interior and exterior SC coordinates. Using these, holding theta,phi constant, you compute proper time along a radial free fall geodesic from both sides. You get finite time to reach the EH, in the limit; you get finite time to the singularity in the continuation. In other coordinates, you don't even need to do this - it is just one continuous line.

This gets quite sticky, as infinities pose a whole host of mathematical problems that most physicists just choose to ignore (not all).

The infinities at the EH are a coordinate artifact. This is routine differential geometry. Unlike QFT which has pure math problems with its foundations, differential geometry is completely rigorous, and GR is expressed in terms of differential geometry.

I am of the opinion that any final theory that integrates quantum mechanics will resolve this issue. There is likely a form of quantum tunneling that occurs once particles get close enough to the event horizon that allows them to make their way in (an, in essence, out) of the black hole in a finite time as observed from us on the outside.

That is probably true, but doesn't justify making false statements about the classical theory.

That said, if you stick strictly to only GR, the outside observer will never "see" the particle cross the event horizon. Information, in all forms, cannot escape from the inside of the BH, be it light or any other effect. Like other people have noted however, the total gravity experienced by the outside observer changes immediately after the particle falls between the observer and the BH anyway. Thus, the only information an outside observer could actually "see" happened long before the particle gets to the event horizon.

That's also fine.

 

[thehangedman]

False. It is a place where this happens in one coordinate system that is ill fitted to this region. In other coordinates this does not happen. On the other hand, even these coordinates you can show that curvature is finite at the EH.

Yes, it happens in one particular coordinate system. I never said it happened in all coordinate systems. This particular coordinate system is used, however, to show what the event horizon is and to do an easy calculation for it. It is HARDLY just an "artifact".

False again. There are interior and exterior SC coordinates. Using these, holding theta,phi constant, you compute proper time along a radial free fall geodesic from both sides. You get finite time to reach the EH, in the limit; you get finite time to the singularity in the continuation. In other coordinates, you don't even need to do this - it is just one continuous line.

Fair enough, but I think it is important to people trying to learn this stuff to realize that what you are doing is a bit of a mathematical trick. The trick is entirely valid, and the difficulty comes in peoples minds when they attempt to reconcile the meaning behind the math. A coordinate system is just a mathematical choice, and in the end people need to think about these things in a more geometrical way, but certain coordinate systems are tied to reference frames, and so have a physical meaning. As such, per the original poster's question, there are really only two coordinate systems we can use that tie directly to the experience being asked about: the one that follows the falling object into the BH, and the one of an external observer (certain assumptions made for simplicity).

I think we all agree (as we should, since it's a known) that the object falling into the BH, from it's own reference frame, just falls straight in with a finite time. We also all know that the light (or, more accurately, information) emitted from the falling object to the external observer would never contain anything that shows it actually cross the EH. That is, the external observer never "sees" the object cross the EH. The effects of gravity still increase, but really that has little to do with the BH swallowing anything.

The infinities at the EH are a coordinate artifact. This is routine differential geometry. Unlike QFT which has pure math problems with its foundations, differential geometry is completely rigorous, and GR is expressed in terms of differential geometry.

Calling something that is highly physically important and the center of the whole issue here a simple "artifact" if ridiculous and misleading. Just because you can make a coordinate shift to push out the "crinkle" doesn't mean it isn't there. You've just hidden it inside your coordinate map. To point, the observer falling into the BH might not experience a "horizon" directly but WILL see some weird effects from the outside world as they close in on that line. The line is still there, it's still relevant, it just expresses itself differently because we are in a different coordinate system.

Infinities are stubborn little things. They can be moved around, twisted and manipulated, but rarely can you ever make them go away.

 

[PAllen]

Calling something that is highly physically important and the center of the whole issue here a simple "artifact" if ridiculous and misleading. Just because you can make a coordinate shift to push out the "crinkle" doesn't mean it isn't there. You've just hidden it inside your coordinate map. To point, the observer falling into the BH might not experience a "horizon" directly but WILL see some weird effects from the outside world as they close in on that line. The line is still there, it's still relevant, it just expresses itself differently because we are in a different coordinate system.

Infinities are stubborn little things. They can be moved around, twisted and manipulated, but rarely can you ever make them go away.

I believe this is mathematically and conceptually invalid. The event horizon is not an artifact. However, there are no geometric discontinuities there, of any kind. All infinities there (rather than at the true singularity) are pure coordinate artifacts. Infinities from coordinate artifacts can occur anywhere. It just happens the for one coordinate system, coordinate infinities happen at the horizon.

Example: Consider a plane, in x,y cartesian coordinates with Euclidean metric. I transform to new coordinates u=xy, v=x. I can't validly cover the y-axis in these coordinates, and the metric has infinities approaching the y-axis in these coordinates. Is there anything wrong with the y axis?

NOTE: I do not say the EH is an artifact. I say any infinities there are an artifact of coordinates ill fitting for this region.

 

[PeterDonis]

Infinities are stubborn little things. They can be moved around, twisted and manipulated, but rarely can you ever make them go away.

Well, then the horizon of a black hole is one of those rare cases; you *can* make the infinity go away, completely, by using a better coordinate chart, and you can prove that all geometric invariants, i.e., all physically meaningful quantities, are finite and well-behaved at the horizon. This is a homework exercise in every GR textbook I'm aware of. It is not at all controversial.

 

[Mike Holland]

Arindamsinha, I had almost the same discussion in my topic "Black Holes - The Two Points of View" a few months back. I agree with your point of view, but have added a few provisos.

A lot of the problem centers around how you define "existence" and "now". Effectively, we live at the point of our past light cone. The light we receive from the universe around us defines our "now". We see the sun "now", but are actually seeing the light that left it 8 minutes ago. And similarly for the stars and galaxies. So when we say that Sirius exists, for example, we are really saying it existed 10 years ago.

Similarly with "existence". We may say that Napoleon is dead, and no longer exists, but an astronomer on a planet 200 light years away aiming his telescope this way would say that he can see Napoleon strutting around on Earh, and therefore he exists. Existence depends very much on one's point of view. We can say that things within our past light cone definitely did exist, as they can have a causal relationship with us, but outside that cone existence depends on the coordinate system chosen to describe the universe.

The result is that using our past light cones as our definition of "now", we can correctly say that Black Holes do not exist "now" in the universe we live in, and there are only slowly collapsing masses where they are forming. And this would apply to any observer at any tme, using that definition of "now", unless they have already (in their timeframe) fallen into a Black Hole. But there are many things going on in the universe which will never enter our past light cones.



Mike

 

[Dale]

Mike, I don't know of ANY standard coordinate system which uses the past light cone to define surfaces of simultaneity. Can you provide a mainstream reference for one?

 

[harrylin]

Arindamsinha, I had almost the same discussion in my topic "Black Holes - The Two Points of View" a few months back. I agree with your point of view, but have added a few provisos. [..]

Hi Mike, I saw some of that discussion, but most of it I could not follow - it was too abstract for me. I hope to be able to incite people to follow Einstein's example and discuss physical "clocks and rods".

A lot of the problem centers around how you define "existence" and "now". Effectively, we live at the point of our past light cone. The light we receive from the universe around us defines our "now". We see the sun "now", but are actually seeing the light that left it 8 minutes ago. And similarly for the stars and galaxies. So when we say that Sirius exists, for example, we are really saying it existed 10 years ago. [..] Similarly with "existence". [..]

Please don't include me in "we"! I mean with "now" and "exists" the same as "simultaneous" according to convention.

Note: PAllen started a topic about simultaneity.

 

[Mike Holland]

Mike, I don't know of ANY standard coordinate system which uses the past light cone to define surfaces of simultaneity. Can you provide a mainstream reference for one?

I am referring to the coordinate system we use all the time in our everyday lives. We observe a supernova, and say that it occurred in 2012. In this everyday sense it was simultaneous with our calendars reading 2012. But as it is 1000 LY away, we calculate that it "really" occurred in 1012. Someone passing by at 0.83c might say it is 500 LY away, and occurred in 1512.

I receive light from trees, the sun, stars, etc, and my mind builds up a view of the world around me, and this view is "now" as far as I am concerned. So I am seeing these things simultaneously, even though some of them may no longer exist - Betelgeus may have exploded a few years ago!

Simultaneity (sp?) depends entirely on the observer or coordinate system, and I rekon my view is as valid as any of them. But I do admit to having another view of "now" based on a theoretical line drawn vertical to my world line. How I draw this line and keep it vertical is based on my understanding of physics - GR in particular. And this theoretical "now" is mine alone, and need not apply to any other observers.

If you go back to Einstein's writings on SR, you will find that right through his work he uses this definition of simulteneity based on paths of light rays, as he proves that it is different for each observer. Is that mainstream enough?

Mike

 

[Dale]

I am referring to the coordinate system we use all the time in our everyday lives.

I am asking for a scientific reference. If you don't have one, then you should stop speculating. Everyday usage is not the same as scientific usage.