How do black holes grow?

arindamsinha

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

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.

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*.

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

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 learnt 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.

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.

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.

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*)

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

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

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

Thanks!

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

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.

It isn't. See above.

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.

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.

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.

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

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.



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...



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

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

I had forgotten to comment on that. In a recent thread I cited some for this topic essential parts:
http://www.physicsforums.com/showpos...5&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

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.

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.

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

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.
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.
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

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

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 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.

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.

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

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.
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

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'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

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.