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

[arindamsinha]

A lot of scientific literature states that black holes 'grow' in size (which I think is equivalent to saying 'grow their Schwarzschild radius or event horizon'). They apparently do so by consuming external matter that falls into them.

However, any matter that does fall toward a black hole, and gets close to the event horizon, should never actually reach the event horizon in the lifetime of the Universe?

I am talking about the point of view of any observers outside the even horizon (e.g. us), not observers who fall into the black hole (who could cross the event horizon in their lifetimes and not even notice the event, ignoring the physical discomfort or deformities caused by tidal forces).

Given the above, how can black holes ever 'grow' in the lifetime of the Universe? (Assuming that some of them have existed from the beginning of the Universe for some reason)

 

[PeterDonis]

A lot of scientific literature states that black holes 'grow' in size (which I think is equivalent to saying 'grow their Schwarzschild radius or event horizon'). They apparently do so by consuming external matter that falls into them.

Yes, that's correct.

However, any matter that does fall toward a black hole, and gets close to the event horizon, should never actually reach the event horizon in the lifetime of the Universe?

The phrase "in the lifetime of the Universe" is coordinate-dependent, and can lead to confusion. A better way to describe what's happening would be to say that light from events at or inside the EH can never get back out to a distant observer. See below for further comment.

I am talking about the point of view of any observers outside the even horizon (e.g. us), not observers who fall into the black hole (who could cross the event horizon in their lifetimes and not even notice the event, ignoring the physical discomfort or deformities caused by tidal forces).

We've had a number of threads on this. You agree that observers who fall into the BH can cross the event horizon in a finite time according to their own clocks, i.e., in a finite proper time. Therefore, matter that falls into the BH can also reach the horizon in a finite proper time. That's all that's necessary for the BH to grow.

It is true that no light signals from any event at or inside the horizon can get back out to the rest of the Universe, as I said above; so an observer far away from the hole will never see anything cross the horizon. If an observer far away from the hole tries to describe the spacetime using the time coordinate most natural to him, he can only describe events from which light signals can reach him; that means that he can't use the time coordinate most natural to him to describe events at or inside the horizon. But that doesn't mean such events don't exist; it just means the distant observer can't describe them using his most natural time coordinate.

 

[arindamsinha]

...so an observer far away from the hole will never see anything cross the horizon...

Thanks for the better description of what I was trying to say.

Now, given your above statement, doesn't it mean that an observer far away can also never see the event horizon of a black hole grow, no matter how long he lives?

This is where I am trying to get some clarity on what it means for a black hole to 'grow'. (a) The notion seems to imply that a very long-lived observer would be able to at some point say that a certain black hole's even horizon has a radius of 'R' and some time later (by his natural time) that the same black hole's radius is now 'R + ΔR'. But (b) it appears that he cannot do so, because he would never see any matter reaching the event horizon to help the black holes mass (and therefore event horizon) grow.

I am not able to mentally reconcile these two (a) and (b), somehow. I am partial to the point of view of the observer far away from the event horizon rather than the one crossing it, as I am identifying ourselves with the observers of the first kind.

 

[PeterDonis]

Now, given your above statement, doesn't it mean that an observer far away can also never see the event horizon of a black hole grow, no matter how long he lives?

If you mean "see" as in "receive light signals from", then no. However, the faraway observer does receive other evidence that the BH has gained mass; he feels an increased gravitational field.

This is where I am trying to get some clarity on what it means for a black hole to 'grow'. (a) The notion seems to imply that a very long-lived observer would be able to at some point say that a certain black hole's even horizon has a radius of 'R' and some time later (by his natural time) that the same black hole's radius is now 'R + ΔR'. But (b) it appears that he cannot do so, because he would never see any matter reaching the event horizon to help the black holes mass (and therefore event horizon) grow.

The key phrase here is "by his natural time". Yes, by his natural time, he never "sees" the BH grow, because his natural time simply can't describe that part of the spacetime, the part at and inside the horizon. But that doesn't mean the part of the spacetime at and inside the horizon doesn't exist, or that matter can't fall into it.

I am partial to the point of view of the observer far away from the event horizon rather than the one crossing it, as I am identifying ourselves with the observers of the first kind.

We *are* observers of the first kind, so it's natural that you would identify us with such observers. However, you need to be careful not to be too "partial" to the point of view of such observers, because the most natural "point of view" for such observers can't describe a portion of the spacetime (at and inside the horizon), so that point of view is a limited one.

 

[PAllen]

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.

 

[arindamsinha]

If you mean "see" as in "receive light signals from", then no. However, the faraway observer does receive other evidence that the BH has gained mass; he feels an increased gravitational field.

Yes, "detect" would be a better description.

The key phrase here is "by his natural time". Yes, by his natural time, he never "sees" the BH grow, because his natural time simply can't describe that part of the spacetime, the part at and inside the horizon. But that doesn't mean the part of the spacetime at and inside the horizon doesn't exist, or that matter can't fall into it.

This is where the crux of my question is.

Then we should never be able to see in our (very extended) lifetimes the creation of a black hole from a massive star's collapse? But apparently that does happen to be observable even in our normal human lifetimes, and certainly if our lifetimes were imagined to be of the order of very long-lived stars...

We *are* observers of the first kind, so it's natural that you would identify us with such observers. However, you need to be careful not to be too "partial" to the point of view of such observers, because the most natural "point of view" for such observers can't describe a portion of the spacetime (at and inside the horizon), so that point of view is a limited one.

This I agree and have no issues with. My questions are entirely from the external observer's point of view, and what they can detect in an ambrosia-extended lifetime.

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.

Agreed from the perspective of "seeing". I have modified this to "detecting" as above. My point is, the external observer will not be able to detect the 'almost horizon' grow unless the actual event horizon also grows, with matter crossing the event horizon in the external observers extended lifetime (eliminating the trivial situation of matter density increase in the space around a black hole because of its strong gravity, even without such matter crossing the event horizon from an external perspective).

However, you can't call it relativity an claim there is only one allowed type of observer.

Agreed, but I believe it is valid to ask a question from the point of view of one of these observers. In this post I am looking at it from the external observers point of view.

...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...

This is where the issue is... from an external observers point of view, new matter cannot fall through the horizon in (his/hers) finite time. Or are you saying that is wrong?

 

[Mike Holland]

The distant observer sees (in a theoretical sense - he can't really see any of this) the contracting mass get more and more time-dilated as it approaches to being a black hole. It will never become a black hole in his time-frame. Further matter falling in will freeze around this matter, continually edging closer and closer, more and more slowly, so that a whole volume around the gravitational radius is effectively frozen.

As this happens, the gravitational radius of the total mass will increase, but the mass within any particular radius will always be just insufficient to form an event horizon at that radius. We end up with a growing region of almost-event-horizon.

So as more mass falls in, the external observer "sees" the almost-horizon grow, but there is no proper horizon to grow within it, just a whole contained region of almost-horizon.

Mike

 

[Bill_K]

arindamsinha, You have a valid point. Discussions about a particle falling into a black hole and never reaching the horizon r = 2M typically assume that the particle is a test particle with mass negligible compared to the mass M of the hole. But it's important to realize that the horizon relates not to the local gravitational field, but to the gravitational field at infinity. It's the radius from which light rays cannot escape to infinity.

If you drop a mass ΔM into the hole, by Gauss's Law the field at infinity becomes that of a mass M + ΔM, and it does not have to wait to do this until the particle arrives at r = 2M. At a given radius, the field will be changed as soon as the particle is within that radius. An outside observer will receive light rays propagating in this greater field, and will never see the particle fall beyond the new horizon, r = 2(M + ΔM).

 

[PAllen]

Agreed from the perspective of "seeing". I have modified this to "detecting" as above. My point is, the external observer will not be able to detect the 'almost horizon' grow unless the actual event horizon also grows, with matter crossing the event horizon in the external observers extended lifetime (eliminating the trivial situation of matter density increase in the space around a black hole because of its strong gravity, even without such matter crossing the event horizon from an external perspective).

I don't know what you mean here. They will see the almost horizon grow (visually, a black shadow against the sky surrounded by Einstein rings will be seen to grow. As for gravitational mass, the orbits of satellites of the BH will be different from before. Thus, no part of your statement makes sense to me.

Agreed, but I believe it is valid to ask a question from the point of view of one of these observers. In this post I am looking at it from the external observers point of view.

Of course it is valid to ask what any observer sees or measures. But it absurd, in relativity, to claim that what one type of observer sees defines the complete reality. An observer in a uniformly accelerating rocket sees part of the universe freeze and stop, forever, as long as they keep accelerating at, e.g. 1 g. Not only see, but this applies to all signals and measurement methods available to the accelerated observer. Do we conclude that this says anything about reality for that part of the universe?

This is where the issue is... from an external observers point of view, new matter cannot fall through the horizon in (his/hers) finite time. Or are you saying that is wrong?

The external observer never sees it actually cross the horizon. They do see and detect the central mass growing. They can ask what their theory predicts about this region they see as frozen - just as the rocket observer can ask what theory predicts about the part of the universe that looks frozen to them.

 

[arindamsinha]

...horizon relates not to the local gravitational field, but to the gravitational field at infinity. It's the radius from which light rays cannot escape to infinity.

Correct me if I am wrong, but this is more the Newtonian/classical view of a 'black hole'. Light rays cannot escape to infinity, and must fall back into that radius/horizon, because the escape velocity is higher than c. However, light rays can go some distance outside the radius/horizon before falling back (and therefore be observed by someone who is close by).

I had this notion for a long time myself, but later came to learn (correctly I hope), that according to GR, that even light rays cannot ever cross back into outer space once they have reached the event horizon. All possible paths (worldlines?) inside lead towards the singularity.

Would love to know if this understanding is correct.

If you drop a mass ΔM into the hole, by Gauss's Law the field at infinity becomes that of a mass M + ΔM, and it does not have to wait to do this until the particle arrives at r = 2M. At a given radius, the field will be changed as soon as the particle is within that radius. An outside observer will receive light rays propagating in this greater field, and will never see the particle fall beyond the new horizon, r = 2(M + ΔM).

This is true for a give region of space, within a certain radius around an arbitrary origin, irrespective of whether it contains a black hole or not.

However, it there is a black hole, and the radius we are talking about is the event horizon, the 'as soon as the particle is within the radius' event will never happen for an external observer, no matter how long he waits for it. That is the point I am trying to bring out.

 

[arindamsinha]

...They will see the almost horizon grow (visually, a black shadow against the sky surrounded by Einstein rings will be seen to grow. As for gravitational mass, the orbits of satellites of the BH will be different from before...

That would be true of a large galaxy as well, as its gravity captures interstellar matter.

For a black hole, an arbitrary region around it (radius > event horizon) can increase in mass and show the above effects as well.

But what of the region of space within the event horizon itself? Since external matter can never reach it, that region can never grow more massive, as seen/detected/computed from an external observer's point of view, I believe.

... But it absurd, in relativity, to claim that what one type of observer sees defines the complete reality...

I am not at all making that claim. I understand that reality may be seen differently by different observer.

I am just looking for an explanation from one particular point of view - how does an observer outside black holes ever see/detect/compute that a given black hole's event horizon is growing, when he cannot see/detect/compute any matter ever reaching the event horizon?

The external observer never sees it actually cross the horizon. They do see and detect the central mass growing. They can ask what their theory predicts about this region they see as frozen - just as the rocket observer can ask what theory predicts about the part of the universe that looks frozen to them.

This seems to state that the event horizon of a black hole never actually grows, from an external observers point of view. However, as more and more mass falls towards the black hole's event horizon, a sufficiently distant observer would notice the mass and gravity of that region increasing. Is that what you are saying?

I am not talking theory here. Lot of astronomical observations have established with reasonable certainty that black holes exist, and they 'grow' by 'eating' external matter - a growth that happens even in as short a period as a human lifetime.

Are you saying that the event horizons of these objects don't actually grow, but they accumulate more and more mass just outside the event horizon, from an external observers point of view?

 

[Mike Holland]

The problem with this thinking is that it assumes we already have a Black Hole and event horizon. But according to the O-S model, it takes an infinite time for the matter to collapse within its Schwarzschild radius, as far as a distant external observer is concerned. So there is no event horizon to grow, just an area of almost-event-horizon to expand.

Astronomical observations could not observe the difference between such an eternally collapsing object and a fully-formed black hole. Time dilation only becomes extreme very close to the SR. With a 10km black hole (3 times the sun's mass), time dilation 1cm away from the event horizon would only be about 1000:1. In addition, the super-massive objects in some galaxies have been observed to have magnetic fields, which rules them out as black holes. So while to all intents and purposes there are black holes in the centres of most, if not all galaxies, in fact according to our clocks and theories they are not quite there yet.

Mike

 

[PeterDonis]

The problem with this thinking is that it assumes we already have a Black Hole and event horizon. But according to the O-S model, it takes an infinite time for the matter to collapse within its Schwarzschild radius, as far as a distant external observer is concerned.

Which does not mean that the event horizon does not form. It just means that light signals from its formation never get back out to the distant observer.

Another way of putting it: claiming that the event horizon never forms because "it takes an infinite time as far as a distant external observer is concerned" is equivalent to claiming that the region of spacetime in which the distant observer's time coordinate is finite is the entire spacetime. This claim is false.

 

[PeterDonis]

Astronomical observations could not observe the difference between such an eternally collapsing object and a fully-formed black hole.

In order to make any sense of this, you would have to have a model of an "eternally collapsing object" that was different than the standard one, so we could verify that both models make the same predictions, at least within our current accuracy of observation. AFAIK no one has come up with such an alternate model. Otherwise you're just saying that we have only one model and therefore only one set of predictions.

 

[PeterDonis]

In addition, the super-massive objects in some galaxies have been observed to have magnetic fields, which rules them out as black holes.

No, it doesn't; it just means that if they're black holes, they're not black holes surrounded by vacuum; they're black holes surrounded by clouds of plasma, which is the currently accepted model. (They're also spinning black holes in the currently accepted model, and their spin induces spin in the plasma, which is what generates the magnetic fields.)

 

[PeterDonis]

Since external matter can never reach it, that region can never grow more massive, as seen/detected/computed from an external observer's point of view, I believe.

I am just looking for an explanation from one particular point of view - how does an observer outside black holes ever see/detect/compute that a given black hole's event horizon is growing, when he cannot see/detect/compute any matter ever reaching the event horizon?

You are equating "see/detect/compute", but they're not equivalent; the distant observer cannot "see/detect" the event horizon forming (because light signals from its formation will never reach him--that's the *definition* of an event horizon), but he *can* "compute" that it forms. That's the whole point of doing computations of gravitational collapse, by solving the Einstein Field Equation. Those solutions "compute" unequivocally that an event horizon *does* form, and that the proper time experienced by an infalling object from any finite radius outside the horizon, to reach the horizon, is finite.

 

[arindamsinha]

Astronomical observations could not observe the difference between such an eternally collapsing object and a fully-formed black hole

In order to make any sense of this, you would have to have a model of an "eternally collapsing object" that was different than the standard one, so we could verify that both models make the same predictions, at least within our current accuracy of observation. AFAIK no one has come up with such an alternate model. Otherwise you're just saying that we have only one model and therefore only one set of predictions.

That's what I was thinking after seeing Mike Holland's response.

That would be a way of getting around the question I have asked. If ideal Black Holes never actually get fully created, but certain regions of space containing matter keep getting closer and closer to the ideal, then there is no reason for them not to be able to grow. The event horizon actually never gets created!

Still, I have not seen this theory anywhere. Is that what the 'O-S model' states? What is the 'OS-model', in brief, to explain to a layman like me?

 

[arindamsinha]

You are equating "see/detect/compute", but they're not equivalent; the distant observer cannot "see/detect" the event horizon forming (because light signals from its formation will never reach him--that's the *definition* of an event horizon), but he *can* "compute" that it forms. That's the whole point of doing computations of gravitational collapse, by solving the Einstein Field Equation. Those solutions "compute" unequivocally that an event horizon *does* form, and that the proper time experienced by an infalling object from any finite radius outside the horizon, to reach the horizon, is finite.

I understand that. There seemed to be too many issues coming up between the terms "see", "detect" and "compute", so I was trying to combine them to state what I mean.

In some senses, "see" may be possible, as explained by the growing shadow.

"Detect" is possible through measuring the gravity growth.

"Compute" is of course possible, based on current theory.

Let us then drop "see" and "detect". My contention is that current theory (GR), does not even allow "computation" of any external matter reaching an event horizon in finite time, from an external observer's point of view, thus the event horizon cannot even be "computed" to be growing from that perspective.

I hope that makes it a little clearer on what my question is.

 

[PeterDonis]

That would be a way of getting around the question I have asked. If ideal Black Holes never actually get fully created, but certain regions of space containing matter keep getting closer and closer to the ideal, then there is no reason for them not to be able to grow. The event horizon actually never gets created!

The word "never" in this context doesn't mean what you think it means. All it means here is "the black hole never gets created at any finite value of the Schwarzschild time coordinate". It does *not* mean "the black hole never gets created, period". That's because the region of spacetime that is covered by finite values of the Schwarzschild time coordinate is not the entire spacetime.

Still, I have not seen this theory anywhere. Is that what the 'O-S model' states?

No. As I said, there is no alternate model of an "eternally collapsing object" in which a black hole never forms (where I'm now using "never" in the strong sense, meaning "never anywhere in the spacetime).

What is the 'OS-model', in brief, to explain to a layman like me?

"O-S" stands for "Oppenheimer-Snyder"; in 1939 Oppenheimer and Snyder published a paper that modeled the collapse of a cloud of "dust" (which is a term for an idealized cloud of matter with zero pressure) under its own gravity, using General Relativity. Their basic model is still valid as a highly idealized (zero pressure in the matter, as I said, and perfect spherical symmetry) qualitative picture of gravitational collapse; it is discussed in most of the major GR textbooks (including Misner, Thorne, & Wheeler, which is where I first learned about it), and in the popular book Black Holes and Time Warps, by Kip Thorne.

For our purposes here, the key point is that this model predicts that the spacetime *does* contain an event horizon and a black hole region. What happens is that the outer surface of the collapsing matter, as it gets smaller and the matter gets denser, eventually becomes a "trapped surface" (this is a modern term and was not used in the original Oppenheimer-Snyder paper); that is, it is a surface from which even outgoing light (light emitted directly radially outward) does not move outward (that is, it doesn't move to a larger radius). Once this happens, the collapsing matter is doomed to continue collapsing all the way to infinite density and infinite spacetime curvature at r = 0, leaving behind an event horizon and a black hole region inside the horizon.

(Actually, the original Oppenheimer-Snyder paper, I believe, did not carry the analysis beyond the instant when the trapped surface forms; in other words, their original analysis was incomplete. But later work has confirmed their analysis and carried it to completion; the result is what I described above.)

 

[PeterDonis]

My contention is that current theory (GR), does not even allow "computation" of any external matter reaching an event horizon in finite time, from an external observer's point of view, thus the event horizon cannot even be "computed" to be growing from that perspective.

Then I'm a bit unclear on your definition of "compute". Read my previous post describing the Oppenheimer-Snyder model; to me, this is a "computation", done by a "distant observer" (after all, that's what we are on Earth relative to any black hole in the universe), which shows that an event horizon *does* form. Why would this not count?

(Or perhaps the problem is the phrase "from an external observer's point of view". The computation I describe shows that no light signal from at or inside the horizon will ever reach the external observer; equivalently, it shows that the region of spacetime in which the external observer's time coordinate is finite does not contain the event horizon or the black hole. If this means the EH doesn't form "from the external observer's point of view", then that's fine, but you have to be very careful not to extend that claim into "the EH doesn't form, period", which is false; the spacetime *does* contain an event horizon and a black hole, and additional matter *can* fall through the horizon and into the black hole. So adopting the "external observer's point of view" forces you to walk a very fine line, to avoid claiming too much. In my experience, most people are not able to walk that line, so it's better, IMO, to just say flat out that the event horizon and the black hole *do* form, and that the "external observer's point of view" is the wrong one to use. But your mileage may vary.)

 

[Mike Holland]

In order to make any sense of this, you would have to have a model of an "eternally collapsing object" that was different than the standard one, so we could verify that both models make the same predictions, at least within our current accuracy of observation. AFAIK no one has come up with such an alternate model. Otherwise you're just saying that we have only one model and therefore only one set of predictions.

When I used the term "eternally collapsing object" I meant it to describe exactly what PAllen described in his post -

"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."

What is observed in this case, and in the case of a fully formed black hole, is a region "blacker than anything else in the universe". But perhaps I should not have used that ECO term, because it has been used elsewhere in other contexts.

You also said "Another way of putting it: claiming that the event horizon never forms because "it takes an infinite time as far as a distant external observer is concerned" is equivalent to claiming that the region of spacetime in which the distant observer's time coordinate is finite is the entire spacetime. This claim is false. ".

I understood this to be the conclusion of the Oppenherimer-Snyder calculations. Where do they allow for any distant observer actually seeing a black hole form in a finite time? OK, I accept that their ideal observer is stationary relative to the forming BH, and an infinite distance fom any space-distorting mass, but I don't believe these conditions affect the conclusion. There are other observers who see the black hole form, but they are local to it, and not distant. So I am not making a claim about all spacetime. And I'm not including spacetime inside a black hole, because that gets too complicated.

Mike

 

[PAllen]

I understand that. There seemed to be too many issues coming up between the terms "see", "detect" and "compute", so I was trying to combine them to state what I mean.

In some senses, "see" may be possible, as explained by the growing shadow.

"Detect" is possible through measuring the gravity growth.

"Compute" is of course possible, based on current theory.

Let us then drop "see" and "detect". My contention is that current theory (GR), does not even allow "computation" of any external matter reaching an event horizon in finite time, from an external observer's point of view, thus the event horizon cannot even be "computed" to be growing from that perspective.

I hope that makes it a little clearer on what my question is.

The problem here is 'time from an external observer's point of view'. If, in fact you talk about seeing and detecting - these are physical and there are not ambiguities. There can be no dispute about what the distant observer sees or detects.

However, as soon as we talk about 'time at a distance' there is great ambiguity. This is not physically measurable. There are perfectly reasonable definitions (and that is all their can be - definitions) of 'time at a distance' such that a distant observer computes that collapse has occurred in finite 'time at a distance' and further infallers reach the singularity in finite 'time at a distance'.

Note that SC coordinate time is a peculiar definition of time for distant observer in the following sense (in classical GR):

- there events I cause, and observers receiving signals from me that are declared never to be simultaneous with any event on my future world line, even carried to infinity.

If you simply modify SC simultaneity to include events caused by an external observer, then you attach finite times to event crossing and arrival at singularity.

 

[PAllen]

Let me make concrete a different definition for times assigned to distant events for distant observer of a collapse leading to spherically symmetric BH. This definition will match SC time for an observer at infinity for events 'near the observer', but will differ more and more for other events. [edit: removed statement about observer not 'near infinity', that is not quite true].

We posit the world line of some static, distant obsever (reference observer). For any event E, we find the event on this observer's world line such that light will reach the chosen event (call clock time for the reference observer for this emission event T0). The chosen event E has some SC r coordinate (r1). The reference world line has some other r coordinate(r0, always). We assign to E a T coordinate of: T0 + (r1-r0)/c.

The defines a perfectly plausible alternate time coordinate for the static observer at r0. It can be combined with SC r, theta and phi coordinates.

With this modification to SC time, it is now true that r0 observer computes finite times for infall event horizon crossings, and infall times of reaching singularity.

 

[PeterDonis]

I understood this to be the conclusion of the Oppenherimer-Snyder calculations.

You understood what to be the conclusion of the O-S calculations? That the distant observer never sees the black hole form, or that it never forms, period? The first *is* the conclusion of the O-S calculations; the second is not.

There are other observers who see the black hole form, but they are local to it, and not distant. So I am not making a claim about all spacetime. And I'm not including spacetime inside a black hole, because that gets too complicated.

Ok, so it looks like your understanding was the first of the two I described above.

 

[arindamsinha]

I have been trying to follow the discussions above and make some sense.

It appears to me now there is some disagreement between interpretations of GR on this point, with three possibilities supported by different scientists, i.e. black holes/event horizons:

1. Do form in finite time for certain observers, but not for certain other observers
2. Do form in finite time for all observers, and
3. Never fully form in finite time for any observer, but keeps getting closer and closer

Is it that there are different interpretations (or even follow-up theories) of GR on this aspect by different scientists?

 

[PAllen]

I have been trying to follow the discussions above and make some sense.

It appears to me now there is some disagreement between interpretations of GR on this point, with three possibilities supported by different scientists, i.e. black holes/event horizons:

1. Do form in finite time for certain observers, but not for certain other observers
2. Do form in finite time for all observers, and
3. Never fully form in finite time for any observer, but keeps getting closer and closer

Is it that there are different interpretations (or even follow-up theories) of GR on this aspect by different scientists?

Speaking only of classical GR, it is crucial to distinguish observables from conventions. I believe there is essentially no dispute about the following observational statements (for the case of collapse, followed by possible later infall):

- An observer riding with collapsing matter or falling in later will cross an EH and reach the singularity in finite time on their watch.

- An observer remaining outside will never see an EH form, nor will they see any later infaller cross an EH (because it won't be seen to form). They will detect (gravitationally) increase in mass of 'black body' as new matter falls in, but no outside measurement will detect any information that an EH has actually formed. However, the delta between this observed almost BH and an eternal BH with actual event horizon, will grow smaller exponentially to the point where no conceivable measurement can distinguish.

As soon as you go from what observers measure to what they might consider to be true based on computation you can make the following statements:

- that the universe contains a BH according to theory (classical GR), is something any observer may compute. They all get the same result that the universe does contain such a thing (given the appropriate collapse).

- There is no objective meaning to 'time at a distance' for events not observed. There is no objective meaning to 'what is over there now'. Depending on different plausible choice for this, you can say a distant observer considers an EH never to form, or to form at some well defined finite time. In either case, it is true that (per computation), the universe as a whole contains a BH with EH.

 

[arindamsinha]

Speaking only of classical GR, it is crucial to distinguish observables from conventions. I believe there is essentially no dispute about the following observational statements (for the case of collapse, followed by possible later infall):

- An observer riding with collapsing matter or falling in later will cross an EH and reach the singularity in finite time on their watch.

- An observer remaining outside will never see an EH form, nor will they see any later infaller cross an EH (because it won't be seen to form). They will detect (gravitationally) increase in mass of 'black body' as new matter falls in, but no outside measurement will detect any information that an EH has actually formed. However, the delta between this observed almost BH and an eternal BH with actual event horizon, will grow smaller exponentially to the point where no conceivable measurement can distinguish.

This is fine. What we (the external observers) have observed in the Universe are really not actual black holes, but so close as to be measurably indistinguishable from one - that makes sense.

The only beef I have about this (not with you, but with GR), is that a 'riding' observer happens to experience an 'event' that an external observer cannot accept will ever happen, no matter how long he waits for it.

As soon as you go from what observers measure to what they might consider to be true based on computation you can make the following statements:

- that the universe contains a BH according to theory (classical GR), is something any observer may compute. They all get the same result that the universe does contain such a thing (given the appropriate collapse).

This is OK, if we substitute 'may contain' for 'contains'. Any black holes that actually exist must have always existed from the Big Bang. A collapsing star since the Big Bang may get asymptotically close, but never achieve a 'hard' event horizon (for external observers).

- There is no objective meaning to 'time at a distance' for events not observed. There is no objective meaning to 'what is over there now'. Depending on different plausible choice for this, you can say a distant observer considers an EH never to form, or to form at some well defined finite time. In either case, it is true that (per computation), the universe as a whole contains a BH with EH.

This part I cannot agree with. For a distant observer, he must conclude an EH never forms, by his clock, in finite time.

Also, he can only conclude that the Universe may contain objects very close to being black holes, but does not contain actual black holes, unless they were formed along with the Big Bang.

 

[harrylin]

That's what I was thinking after seeing Mike Holland's response.

That would be a way of getting around the question I have asked. If ideal Black Holes never actually get fully created, but certain regions of space containing matter keep getting closer and closer to the ideal, then there is no reason for them not to be able to grow. The event horizon actually never gets created!

Still, I have not seen this theory anywhere.

As a result of a little "Googling" from my part this was recently discussed in several other black hole threads, for example from here:
- https://www.physicsforums.com/showthread.php?p=4129133
and from here:
- https://www.physicsforums.com/showthread.php?p=4163727
and from here:
- www.physicsforums.com/showthread.php?p=4164194
(and also a little in here:
- www.physicsforums.com/showthread.php?t=647627)

Thus it's a matter of interpretation of models, and the interpretation that you are looking for apparently began with Einstein's 1939 paper. In that interpretation a falling observer will not experience a falling through the horizon ("The essential result of this investigation is a clear understanding as to why the "Schwarzschild singularities" do not exist in physical reality").

For me that topic has been sufficiently discussed now, and it's sufficiently clear, so I'll leave it up to you in your thread. :tongue2:

PS: I see your last remark in post #27. Just like me, your beef is not with GR but with an interpretation of GR. That is a big difference.

 

[PeterDonis]

The only beef I have about this (not with you, but with GR), is that a 'riding' observer happens to experience an 'event' that an external observer cannot accept will ever happen, no matter how long he waits for it.

The external observer will never directly *observe* the "event" (of the EH forming and something falling into it), but that doesn't mean he can't *accept* that it will happen. He can compute that it will happen using a well-supported scientific theory; why shouldn't that be sufficient grounds for him to "accept" that it will happen, even though he can't directly observe it?

Any black holes that actually exist must have always existed from the Big Bang.

Black holes can't be formed this way.

A collapsing star since the Big Bang may get asymptotically close, but never achieve a 'hard' event horizon (for external observers).

You have to be very, very careful about that word "never". See what I said above about the external observer "accepting" that the BH forms even though he can't directly observe it.

This part I cannot agree with. For a distant observer, he must conclude an EH never forms, by his clock, in finite time.

He can conclude that no EH forms in a finite time by his clock, yes. But you appear to be putting in an additional premise with the word "never": that *any* event, anywhere in the universe, must have a finite time, by his clock, associated with it. That is false; there is a whole region of spacetime (the EH and the BH region inside it) that *cannot* be assigned a finite time on the distant observer's clock; at least, not if he uses the most natural method of assigning times on his clock to events which are spatially distant from him. As PAllen pointed out, the real point here is that in GR, there is no unique method of doing that; there are multiple ways of assigning times on the distant observer's clock to events, and no one of them is "right". That is why we focus on things that don't depend on arbitrary decisions like how we assign times to distant events; when we focus on those things, we find that (according to our best current theoretical understanding) there *is* an event horizon and a black hole, even though the distant observer can't see it.

 

[PAllen]

This is fine. What we (the external observers) have observed in the Universe are really not actual black holes, but so close as to be measurably indistinguishable from one - that makes sense.

The only beef I have about this (not with you, but with GR), is that a 'riding' observer happens to experience an 'event' that an external observer cannot accept will ever happen, no matter how long he waits for it.

This is s feature of the belief system of the observer not an issue of physical theory. Why wouldn't a distant observer accept that what they calculate for an infalling clock's own experience is true? The physical theory has no conflicting events at all. It simply has a feature that no observer can detect all events in the universe. Why is this such a bizarre concept?

This is OK, if we substitute 'may contain' for 'contains'. Any black holes that actually exist must have always existed from the Big Bang. A collapsing star since the Big Bang may get asymptotically close, but never achieve a 'hard' event horizon (for external observers).

Again, a statement that only one class of observers defines reality is at odds with GR. GR and SR say all observers measurements are meaningful. An external observer can easily compute what in infalling observer detects. There is no conflict with what an external observer detects (that is, no conflicting observation of the same event). There is, again, simply the feature that one observer experiences events that another observer cannot detect. I don't believe you generally assume, in life, that if you can't detect something it didn't happen.

This part I cannot agree with. For a distant observer, he must conclude an EH never forms, by his clock, in finite time.

Also, he can only conclude that the Universe may contain objects very close to being black holes, but does not contain actual black holes, unless they were formed along with the Big Bang.

And this is true only if you say there is a law against the external observer computing predictions from theory about events they cannot see. That is an absurd prohibition. Note, we agree about the observational statements, which I listed first in the post you respond to. But you asked about what they may compute. Why is an external physicist prohibited from computing predicted events that they cannot observe (but someone else, e.g. an infaller, can)?

Further, independent of observations, computationally there are many ways to relate distant events in the universe as happening at your 'now'. Both GR and SR say this is a matter of convention not physics. There are numerous simultaneity conventions a distant observer may choose such that they compute an EH and singularity have formed [I gave a simple, physical, definition of one in my post #23]. This in no way contradicts that they also compute they will never detect any information from these events.

 

[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.