Black Holes - the two points of view.

[Mike Holland]

Well, I guess its time this topic was put to bed. I don’t seem to have convinced anyone of my views, and nobody has convinced me of theirs. So I guess that makes us even!

Generally the arguments I have been presented with follow the lines of “Black Holes exist, and I am wrong because …”

1. I have misinterpreted the mathematicians.
All my quotes were in English, and where necessary, had been translated by others. English is my home language, and no interpretation was necessary as I was simply quoting what they had said.

2. You can’t trust words, You can only trust the maths.
But you need words to explain what the maths means. Pg = N/Tv doesn’t mean a thing until words are used to explain what Pg etc means.

3. General Relativity fails at the Event Horizon.
No it doesn’t. It only fails, if at all, at the singularity in the centre of the Black Hole.

4. Schwarzschild coordinates don’t work at the Event Horizon.
Not quite. Schwarzschild is valid outside the Black Hole, right up to the Event Horizon.

5. Other coordinate systems, eg.Einstein-Finklestein and Kruskal-Szekeres coordinates, cover the whole continuum both inside and outside the Event Horizon.
But outside the EH they become Schwarzschild anyway, right up to the Event Horizon. They don't show that a BH will form in a finite time for a distant observer.

6. You can get an Event Horizon 1 light year behind you by accelerating at 1g.
But this tells us nothing about time dilation observed for a distant collapsing superstar. You can stop accelerating, and reverse direction, but you can’t reverse a Black Hole.

7. The calculations are based on ideal conditions such as spherical symmetry, and any small deviation from symmetry would cause a Black Hole to form rapidly.
Every improvement in the calculations to date - adding pressure, rotation, computer simulations, has so far produced the same result. Where is the evidence for small perturbations producing a different result? This argument was presented by Saul Teukolsky, with nothing to back it up.

8. Time Dilation is a redshift illusion caused by the delay of successive photons leaving a falling object.
Wrong. If the object was hovering near the EH, it would be time-dilated, and we would see a redshift which has nothing to do with the time photons take, as all photons would take the same time to reach us. Time dilation is real, and the distant observer's take on things is just as valid as that of the guy falling into a Black Hole.

9. Calculations show that it is possible for naked singularities to form.
According to Saul Teukolsky, who did the calculations, they only work for axisymmetrical objects. The next time you see a large can of beans (his example) in the centre of a galaxy, let me know.

Nobody has yet produced a calculation showing that a Black Hole can form in a finite time for a distant observer. All the calculations so far show that time dilation wins and a Black Hole only forms after an infinite time as a frozen star, as far as any distant observer is concerned. Not one of my critics has produced calculations to prove me (and Oppenheimer, et al) wrong.

I rest my case.

Many thanks to PAllen, PeterDonis, and all the other contributors, who have taught me a lot, but haven’t changed my mind.

Mike

 

[Dale]

Generally the arguments I have been presented with follow the lines of “Black Holes exist, and I am wrong because …”

I don't think that anyone has asserted the existence of black holes. Merely explained that your reasons for asserting their non-existence are wrong.

4. Schwarzschild coordinates don’t work at the Event Horizon.
Not quite. Schwarzschild is valid outside the Black Hole, right up to the Event Horizon.

Up to, but not including the event horizon. In GR coordinate charts are defined on open subsets of the manifold, so they do not include the boundary. In the case of Schwarzschild coordinates they do not include the event horizon, nor any of the events on the interior of the event horizon.

5. Other coordinate systems, eg.Einstein-Finklestein and Kruskal-Szekeres coordinates, cover the whole continuum both inside and outside the Event Horizon.
But outside the EH they become Schwarzschild anyway, right up to the Event Horizon. They don't show that a BH will form in a finite time for a distant observer.

This is simply false.

6. You can get an Event Horizon 1 light year behind you by accelerating at 1g.
But this tells us nothing about time dilation observed for a distant collapsing superstar.

True, but it does tell you something about the nature of event horizons. Specifically, that the existence of an event horizon does not imply the non-existence of events beyond the horizon. It also shows that you cannot determine the existence or non-existence of an event by exclusively considering the information received by a single "preferred" observer. All observers are equally valid.

Nobody has yet produced a calculation showing that a Black Hole can form in a finite time for a distant observer. All the calculations so far show that time dilation wins and a Black Hole only forms after an infinite time as a frozen star, as far as any distant observer is concerned. Not one of my critics has produced calculations to prove me (and Oppenheimer, et al) wrong.

I haven't looked into this in detail, but isn't there a period of time during which the event horizon exists, and is a smaller radius than the ball of dust. During this time I thought that the EH is expanding and particles cross the event horizon in a finite amount of coordinate time.

And again, even if you are correct, you forget that a distant observer is not a "preferred" observer in any way, so his measurements are not the sole arbiter of existence or non-existence.

 

[Mike Holland]

True, but it does tell you something about the nature of event horizons. Specifically, that the existence of an event horizon does not imply the non-existence of events beyond the horizon. It also shows that you cannot determine the existence or non-existence of an event by exclusively considering the information received by a single "preferred" observer. All observers are equally valid..

I have never denied anything about the interior of a Black Hole. What I have said is that the existence or non-existence of that space depends on your point of view. And I have said over and over that all viewpoints (reference frames) are equally valid.

But we can more-or-less group those equally valid observers into two sub-groups - those outside any Black Holes, and those on the Event Horizons or inside. For the latter group, Event Horizons exist and the space (if you can call it that, with two space dimensions and a (null) time dimension) exist. But all the mathematics produced so far says that for the former sub-group Black Holes do not exist and they will take an infinite time to form. This sub-group is a little bit special just because we are in it, and that is why I say WE cannot say Black Holes exist - they don't in our time-frame! Not until OUR clocks read infinity!

I understand the argument that just before a Black Hole forms, there are photons emitted in the centre which will never be able to escape in time, so there is effectively an Event Horizon growing in the centre. But I don't believe this quite cuts the cake as an EH, because photons are not being turned back there, and there is not infinite time dilation there - the gravitational potential is not high enough yet.

Mike

 

[Dale]

But we can more-or-less group those equally valid observers into two sub-groups - those outside any Black Holes, and those on the Event Horizons or inside.

This is fine.

all the mathematics produced so far says that for the former sub-group Black Holes do not exist

This is false on multiple counts. First, the existence or non-existence of an event in the manifold is a property of the topology of the manifold itself, not a property of any coordinate chart which may be imposed on top of the manifold. Second, even if you replaced "do not exist" by something like "are not covered by their coordinate chart" the statement is still false since the EH and the black hole are in fact covered by many coordinate charts of observers which are outside the black hole, e.g. free-falling observers which are outside.

I think that the first point is the key conceptual error you are making. Whether or not something exists has nothing to do with any coordinate chart, so your argument based on Schwarzschild coordinates is completely irrelevant to the question of the existence of the event horizon.

 

[Mike Holland]

First, the existence or non-existence of an event in the manifold is a property of the topology of the manifold itself, not a property of any coordinate chart which may be imposed on top of the manifold. Second, even if you replaced "do not exist" by something like "are not covered by their coordinate chart" the statement is still false since the EH and the black hole are in fact covered by many coordinate charts of observers which are outside the black hole, e.g. free-falling observers which are outside.

I think that the first point is the key conceptual error you are making. Whether or not something exists has nothing to do with any coordinate chart, so your argument based on Schwarzschild coordinates is completely irrelevant to the question of the existence of the event horizon.

I think the only problem here is the use of English. I believe it is wrong to say "dinosaurs exist". WE from out point in space-time can only say they DID exist. Similarly I cannot say my great-great-grandsons exist. I can only say they WILL exist (I hope!)

These things may all exist in the manifold, but relative to our "now" in the manifold we cannot say they DO exist NOW. Remember that in all my discussion I am talking about the space-time that WE are living in NOW.

Mike

Edit: I don't think we have a disagreement here. You are looking at the plenum from God's perspective, so to speak, while I am looking at it from the viewpoint of a humble mortal!

 

[DrGreg]

I think the only problem here is the use of English. I believe it is wrong to say "dinosaurs exist". WE from out point in space-time can only say they DID exist.

That's fair enough, but if you said "dinosaurs don't exist", I think that, the way language is commonly used, many people could interpret that to mean that you thought dinosaurs have never existed, though you really meant, "they no longer exist now".

The situation with black holes is a little more subtle. Although anyone who stays outside an event horizon cannot see what is inside it (or "will be inside it"?), you do have the option to go inside and have a look (technology permitting) if you want to, within a finite amount of your own time (though the rest of us will never hear from you again). So is it really fair to say the inside "doesn't exist"?

You may say, we have no direct experimental evidence to prove what happens inside an event horizon, which is true enough, but we do have a theory that predicts what ought to happen; we are talking about "existence" in the context of what the theory predicts.

 

[Mike Holland]

Ok, DrGreg, then what I should be saying for us outside viewers is "don't exist YET". Black holes will exist, in our infinite future, or in our very finite future if we fall into supermassive collapsing stars.

Mike

 

[PeterDonis]

Remember that in all my discussion I am talking about the space-time that WE are living in NOW.

But NOW does not have an invariant meaning; it depends on your choice of simultaneity convention. There are ways to choose a simultaneity convention so that the black hole at the center of the Milky Way galaxy exists NOW.

 

[Dale]

I think the only problem here is the use of English. I believe it is wrong to say "dinosaurs exist". WE from out point in space-time can only say they DID exist. Similarly I cannot say my great-great-grandsons exist. I can only say they WILL exist (I hope!)

These things may all exist in the manifold, but relative to our "now" in the manifold we cannot say they DO exist NOW. Remember that in all my discussion I am talking about the space-time that WE are living in NOW.

Roughly speaking, you can divide the spacetime up into three regions, the interior of the future light cone, the interior of the past light cone, and the exterior of the light cone. Events that will exist are in the first region, events that did exist are in the second, and all other events can be considered to exist "now", in a coordinate independent sense. In the Schwarzschild spacetime, the interior of the black hole is in the [STRIKE]second[/STRIKE] first and third regions, so it should be considered to exist now and in the future. If anything, you would say only that it did not exist in the past.

 

[arindamsinha]

Thinking out of the box (or stupidly?) black holes cannot get created in the lifetime of the Universe. Either they always existed from the beginning of the Universe, or they do not exist. Any black holes that exist, cannot grow into more massive black holes by acquiring mass.

Consider the theory of creation of a black hole from the collapse of a massive star because of its own gravity. To begin with, it is all ordinary matter. At some stage of collapse then, it must 'create' a core black hole, with matter passing through the event horizon to 'grow' the black hole further.

The problem is, a black hole cannot grow by acquiring mass from outside the event horizon. Ordinary matter has 'extent', however small. So when the leading edge of such matter reaches (or tries to reach forever?) the event horizon, the rest of the matter has to protrude outside of the even horizon, because of the 'extent' of the matter. A black hole would therefore get quickly covered by a film of interstellar material, parts of which will remain outside the even horizon.

As more matter falls in towards the event horizon, the existing film of matter outside the even horizon will prevent them from reaching the event horizon. So, the black hole will soon get covered by increasingly thick spherical shells of ordinary matter. It will first grow into something like a planet, and then possibly rapidly into a star, given its strong gravity!

Now, if a black hole cannot grow using ordinary matter, how can it even form the 'core' in the first place?

 

[Mike Holland]

Roughly speaking, you can divide the spacetime up into three regions, the interior of the future light cone, the interior of the past light cone, and the exterior of the light cone. Events that will exist are in the first region, events that did exist are in the second, and all other events can be considered to exist "now", in a coordinate independent sense. In the Schwarzschild spacetime, the interior of the black hole is in the second and third regions, so it should be considered to exist now and in the future. If anything, you would say only that it did not exist in the past.

Slight confusion here. No light can leave the interior of a Black Hole, so how could any light from the interior be in my or your past light cone (second region)?

Similarly, you can choose the past light cone for any point in the third region, and nothing will have entered this cone from the inside of an event horizon.

So the inside of a black hole is not in the past light cone of any observer remote from the black hole.

The inside of a black hole is never in the past light cone of any observer, now or in a trillion years time, unless the observer falls into the black hole. The inside exists only for the inside. It does not exist for outside observers.

Mike

 

[Mike Holland]

But NOW does not have an invariant meaning; it depends on your choice of simultaneity convention. There are ways to choose a simultaneity convention so that the black hole at the center of the Milky Way galaxy exists NOW.

If the hole exists now, then it should be in our past light cone in about 27,000 years. Now you please tell me how long it takes for a photon to escape from the event horizon and become part of our past light cone. What simultaneity convention will get it here in 27,000 years?

Edit: I think you will find that as the supermassive object at the centre of the galaxy enters our past light cone, the cone becomes distorted - photons don't simply fly from there to here at c anymore, and photons from the EH never get here.

Mike

 

[Dale]

Slight confusion here. No light can leave the interior of a Black Hole, so how could any light from the interior be in my or your past light cone (second region)?

Oops, good catch. I messed up my own numbering. I meant that the interior was in the first and third regions (future and present), not second and third (past and present). I have corrected it above.

The inside exists only for the inside. It does not exist for outside observers.

No, remember your emphasis on the proper tense. For outside observers the inside exists in the present and will exist in the future. For outside observers it did not exist in the past.

 

[Dale]

If the hole exists now, then it should be in our past light cone in about 27,000 years.

No. Its existence or non existence "now" has nothing to do with some future events past light cone. It has only to do with whether or not it is in the manifold in the region which is space like separated from our present event. Chances are that we will not even exist in 27000 years to have a past light cone.

 

[Mike Holland]

No. Its existence or non existence "now" has nothing to do with some future events past light cone. It has only to do with whether or not it is in the manifold in the region which is space like separated from our present event. Chances are that we will not even exist in 27000 years to have a past light cone.

You are trying to ignore time and only look at space separation to decide whether something exists "now". But from this god-like perspective where time is just another dimension, all things exist in the eternal "now".

All the calculations show that there is a separation of infinite time in addition to the separation of finite space between an event horizon and its insides, and the remote observer. Because you insist on believing in Black Holes, you choose to ignore this. Do you not believe in gravitational time dilation?

As I have said before, I am looking at ther world from our perspective, and light cones are relevant in deciding what is in our past and what will be in our past. The insides of Black Holes willl never be in our past light cones (or anyone else's), wherever they might exist in the manifold, as long as we don't make the stupid mistake of falling into one.

Mike

 

[Dale]

You are trying to ignore time and only look at space separation to decide whether something exists "now". But from this god-like perspective where time is just another dimension, all things exist in the eternal "now".

This is incorrect, there is not just one region. As I explained before there are three regions, "future" (interior of future light cone), "past" (interior of past light cone), and "now" (exterior of future light cone). All other causal distinctions are coordinate-dependent.

All the calculations show that there is a separation of infinite time in addition to the separation of finite space between an event horizon and its insides, and the remote observer. Because you insist on believing in Black Holes, you choose to ignore this.

Only in Schwarzschild coordinates. Not in many other coordinate systems. I am not ignoring the infinities at the horizon in the Schwarzschild coordinates, merely pointing out that those infinities do not exist in other coordinates.

You state that "all the calculations show ...", and that is simply false. Only calculations based on Schwarzschild coordinates show what you claim. Calculations based on other coordinates show that the interior does exist now.

As I have said before, I am looking at ther world from our perspective, and light cones are relevant in deciding what is in our past and what will be in our past. The insides of Black Holes willl never be in our past light cones (or anyone else's), wherever they might exist in the manifold, as long as we don't make the stupid mistake of falling into one.

Agreed. Therefore as I said before, if you insist on talking with proper tenses then you can claim that the black hole did not exist in the past. But you cannot make the claim that it does not exist now and will not exist in the future.

 

[Mike Holland]

You state that "all the calculations show ...", and that is simply false. Only calculations based on Schwarzschild coordinates show what you claim. Calculations based on other coordinates show that the interior does exist now.

Hooray! This is what I have been asking for all along. Please direct me to some publications where these calculations for a remotely observed collapsing mass have been published. I am sick of being told by everyone that they exist, without any follow-up references.

Everywhere I've looked at other coordinate systems, they all seem to be the same as Schwarzschild coordinates outside the event horizon.

Mike

 

[Dale]

I am sick of being told by everyone that they exist, without any follow-up references.

Everywhere I've looked at other coordinate systems, they all seem to be the same as Schwarzschild coordinates outside the event horizon.

I linked you right to the Wikipedia pages on 4 alternative coordinate systems in the Schwarzschild spacetime back in post 16:
https://www.physicsforums.com/showpost.php?p=4029984&postcount=16

Don't try to claim that I have been holding out on you if you didn't bother to read the references I provided.

 

[PeterDonis]

If the hole exists now, then it should be in our past light cone in about 27,000 years.

This does not follow. In a flat spacetime it would; but our spacetime is not flat, it's curved, and it's curved in a way that makes the apparent logical implication in your statement invalid.

What *is* in our past light cone is the object (or objects) that originally collapsed to form the black hole. And what will be in our past light cone 27,000 years from now is a somewhat larger portion (i.e., closer to the horizon) of the history of that object (or objects) prior to it crossing the horizon.

 

[Austin0]

Hooray! This is what I have been asking for all along. Please direct me to some publications where these calculations for a remotely observed collapsing mass have been published. I am sick of being told by everyone that they exist, without any follow-up references.

Everywhere I've looked at other coordinate systems, they all seem to be the same as Schwarzschild coordinates outside the event horizon.

Mike

Hi
I don't know enough GR to have an opinion one way or the other in this fascinating controversy but I do have a question.

Given an infalling atom. At the point where the metric indicates infinite dilation doesn't it also indicate infinite radial contraction? If this is the case then it would seem that the distinction between "at" the horizon and "in" the horizon becomes meaningless.
So larger structures would not maintain extent beyond the horizon but would, an atom at a time, become compacted to become effectively a dimensionless part of the horizon.

Based on your interpretation i get a picture of the horizon being an abstract geometric surface. A smooth, dimensionless and static boundary of absolute impenetrability.
While I can't argue against such a construct it doesn't seem as realistic as a more QM picture of a dynamic region with a certain degree of fuzzy dimensionality due to uncertainty,vacuum flux and reaction to the the changes occurring both within and without.
If there is no abstract dimensionless boundary then there is no abstract dimensionless mathematical point of infinite gamma but rather a fuzzy uncertain transition from outside to inside along the lines of electron tunneling. Just a thought.

 

[Mike Holland]

Austin0, from a remote point of view your picture is correct, but what is stopping collapse there is the stopping of time so that nothing can happen there. But remember that this is in a remote observer's timeframe. If you are falling into the collapsing mass that is becoming a Black Hole, you will not experience the time dilation because you are similarly dilated, and you will fall through the Event Horizon very quickly. The tricky part is getting your mind around time flowing very differently for different viewers, and both being equally valid.

Regarding the quantum fuzziness, I am stll waiting for a theory of quantum gravity to resolve this. Does the time dilation quell the fuzziness, or does the fuzziness make the location of the Event Horizon indeterminate? I don't know.


Dalespam, I have read the references you provided. Einstein-Finklestein coordinates are the same as Schwarzschild coordinates outside the Event Horizon, so they make no difference to the prediction that gravitational collapse will take an infinite time in a remote viewer's reference frame. The other systems just assign different scaling factors to space and time so that the numbers look different. It is like setting T = 10 + 1/t, so that a Black Hole forms at 10 o'clock, and my new "time" is continuous through 9, 10, 11 0'clock. They don't at any point show that the Schwarzschild calculations are incorrect. My T makes no difference to t being infinite.

Anyway, I was not asking for different coordinate systems to look at the situation. I was asking for actual calculations done using these coordinates to show that a Black Hole would form in a finite time, contrary to Schwarzschild. You have not provided this, and I don't believe any such calculation has been done.


And last, but not least, PeterDonis :
"This does not follow. In a flat spacetime it would; but our spacetime is not flat, it's curved, and it's curved in a way that makes the apparent logical implication in your statement invalid.
What *is* in our past light cone is the object (or objects) that originally collapsed to form the black hole. And what will be in our past light cone 27,000 years from now is a somewhat larger portion (i.e., closer to the horizon) of the history of that object (or objects) prior to it crossing the horizon."

That is more-or-less the point I was trying to make. If our "now" is defined by our past light-cone, then a Black Hole will never enter it, because of the time delay of photons escaping from near the Event Horizon. In this sense, Black Holes do not exist because we can never see them. But this ignores the added factor or time dilation which prevents the Black Hole from forming in a finite time anyway.

"But NOW does not have an invariant meaning; it depends on your choice of simultaneity convention. There are ways to choose a simultaneity convention so that the black hole at the center of the Milky Way galaxy exists NOW."

In simple, practical terms, "now" is my past light cone, but in a more theoretical sense it is a line drawn perpendicular to my world line in a space-time diagram. As you say, I need a simultaneity convention to determine what points/events lie on this line. Or in other words, I need to choose my coordinate system before I can draw my vertical line. But I challenge you to invent a convention that will change the infinity that comes out of Schwarzschild coordinates into a finite time. Multiply it be anything you like (except zero!), add or subtract anthing you like, and it will still be infinity.

Mike

 

[PeterDonis]

At the point where the metric indicates infinite dilation doesn't it also indicate infinite radial contraction?

No. But rather than use ambiguous English words, it's better to describe the math. In Schwarzschild coordinates, at the horizon, r = 2M, the metric coefficient g_tt goes to zero, and the metric coefficient g_rr goes to infinity.

"Infinite time dilation" refers to g_tt going to zero, but that's really a misnomer; a better description would be to say that at the horizon, a line element with only dt nonzero is not timelike any longer; it's null, or lightlike. (Strictly speaking, in Schwarzschild coordinates the line element is undefined, since g_rr is infinite, but there are other ways to describe "a line element on the horizon with only dt nonzero" that don't depend on Schwarzschild coordinates. One way is to look at the vector \partial_t, which can be defined as a vector field on the spacetime independent of coordinates, and see that that vector becomes null at the horizon, instead of timelike.) Since such a line element is no longer timelike at the horizon, it doesn't describe a "time interval" at all.

"Radial contraction" is also a misnomer; g_tt going to infinity does *not* mean that physical radial distances are "infinitely contracted". It means that, as you get closer and closer to the horizon, a given increment of radial coordinate dr corresponds to more and more physical radial distance. But it also means that, as you get closer and closer to the horizon, a line element with only dr nonzero gets closer and closer to being null instead of spacelike. (Or, equivalently, the vector \partial_r gets closer and closer to being null.) And once again, since such a line element is no longer spacelike at the horizon, it doesn't describe a "spatial length" at all.

To actually find out what happens to objects that reach the horizon, or fall inside, you have to stop using Schwarzschild coordinates, and start using some method of description that doesn't have these issues at the horizon. One option that fixes the "spatial length" problem is Painleve coordinates: the Painleve radial coordinate is spacelike all the way down to r = 0. The only well-known chart I'm aware of that has a coordinate that's timelike all the way down to r = 0 is the Kruskal chart. But there are other ways of describing timelike vectors below the horizon.

 

[PeterDonis]

That is more-or-less the point I was trying to make. If our "now" is defined by our past light-cone

It is, in the sense that our "now" at any given event consists of those events that are *outside* our past light cone, and also outside our future light cone.

then a Black Hole will never enter it, because of the time delay of photons escaping from near the Event Horizon.

No, you're getting the definition of "now" mixed up. See above. The correct statement is that the region inside the horizon can never be in our past light cone if we are outside the horizon. A portion of the region inside the horizon is in our future light cone, at least as long as the BH is not close to finally evaporating; the rest of the region inside the horizon is in our "now".

In simple, practical terms, "now" is my past light cone

No, it isn't. See above.

But I challenge you to invent a convention that will change the infinity that comes out of Schwarzschild coordinates into a finite time.

I don't have to invent any; there are already at least three that I know of: ingoing Painleve coordinates, ingoing Eddington-Finkelstein coordinates, and Kruskal coordinates. All of those charts embody a simultaneity convention that removes the infinity at the horizon and includes many surfaces of simultaneity that cross the horizon.

 

[Austin0]

Austin0, from a remote point of view your picture is correct, but what is stopping collapse there is the stopping of time so that nothing can happen there. But remember that this is in a remote observer's timeframe. If you are falling into the collapsing mass that is becoming a Black Hole, you will not experience the time dilation because you are similarly dilated, and you will fall through the Event Horizon very quickly. The tricky part is getting your mind around time flowing very differently for different viewers, and both being equally valid.

Regarding the quantum fuzziness, I am stll waiting for a theory of quantum gravity to resolve this. Does the time dilation quell the fuzziness, or does the fuzziness make the location of the Event Horizon indeterminate? I don't know.

Mike

You seem to be contradicting yourself. On one hand you posit nothing can pass the horizon because time dilation becomes infinite and coordinate velocity becomes c which is zero at that point. Then you talk about about an observer passing through the horizon very quickly.

Assuming this observer was conscious he might not be aware of the time dilation ,but as it is a feature of the spacetime geometry at that location, it is not that it would not be in effect.

Infinite dilation. To me a single instant that is infinitely dilated, I.e extended in duration, is totally equivalent to a clock ticking away to an infinite reading. They both take effectively forever. Which is a longer infinity? , perhaps Cantor could say.

it seems to me that reaching this point is equivalent to actually reaching c in flat spacetime. Time no longer has any meaning. Whether or not this observer is moving or not would not be internally determinable if both his clock and brain activity had come to a stop.
So if we assume that motion stops at the horizon,collapsing matter etc. this would seem to have to include your observer. So we might say he is trapped there for eternity but when the end of days comes and he passes inside it will have happened quickly , having taken zero time by his stopped clock?
Or are you saying that matter does pass the horizon and black holes do form in a short finite time but that it is unobservable from the outside?
About your idea that time dilation would retard or prevent radial contraction at the boundary.
You may be right but I would think that both dilation and contraction were effects of the underlying geometry which is the cause. SO contraction would occur simply because of being at that location wrt the geometry and would not be subject to slowing through dilation which is just another independent effect of that geometry.

Well thanks for a very interesting and provocative thread.

I have no idea of the answer , my only belief is that there would be a singular dynamic geometric entity and so there would be a singular actuality independent of observation and coordinate choices.

 

[Mike Holland]

I have no idea of the answer , my only belief is that there would be a singular dynamic geometric entity and so there would be a singular actuality independent of observation and coordinate choices.

Sorry, but physics just doesn't work that way. Time passes differently for different observers. Our clocks run slow because of Earth's gravity. A clock in a high-altitude plane or a satellite runs faster. This has been measured. And this is what is predicted by Einstein's theories.

Mike

 

[Austin0]

Sorry, but physics just doesn't work that way. Time passes differently for different observers. Our clocks run slow because of Earth's gravity. A clock in a high-altitude plane or a satellite runs faster. This has been measured. And this is what is predicted by Einstein's theories.

Mike

`Yes of course this is simple fact. What could lead you to believe that I was not aware of or questioned this obvious reality.
Do you somehow question that this is the observable manifestation of a singular underlying geometry?
I am curious why you ignored everything in my post except a casual parting aside which you seem to have reinterpreted to have absurd implications.

 

[Dale]

Einstein-Finklestein coordinates are the same as Schwarzschild coordinates outside the Event Horizon

I don't know how you could possibly have actually read the link and gotten this so egregiously wrong.

T=t+R \; ln \left| \frac{r}{R}-1 \right| \neq t

The other systems just assign different scaling factors to space and time so that the numbers look different. It is like setting T = 10 + 1/t, so that a Black Hole forms at 10 o'clock, and my new "time" is continuous through 9, 10, 11 0'clock.

Yes, that is exactly the point. Your objection amounts to a complaint that some arbitrary number, t, goes to infinity, but that arbitrary number has no physical significance and can therefore be replaced by equally arbitrary number, T, which does not go to infinity.

They don't at any point show that the Schwarzschild calculations are incorrect. My T makes no difference to t being infinite.

The Schwarzschild calculations are correct, t is infinite. But t is a completely arbitrary label and has no physical significance.

Do you believe that changing coordinate systems can make something start or stop existing?

Anyway, I was not asking for different coordinate systems to look at the situation. I was asking for actual calculations done using these coordinates to show that a Black Hole would form in a finite time, contrary to Schwarzschild. You have not provided this, and I don't believe any such calculation has been done.

The Schwarzschild spacetime is static, representing a static eternal black hole, not the formation of a black hole. None of the coordinates listed, neither Schwarzschild nor the others, describe the formation.

However, what you can show in the Schwarzschild spacetime is that a small amount of matter can indeed fall in and cross the EH. If you use Schwarzschild coordinates in the Schwarzschild spacetime you find that t is infinite. In the other coordinate systems you find that T is finite. In all coordinate systems you find that τ is finite.

 

[Mike Holland]

So if we assume that motion stops at the horizon,collapsing matter etc. this would seem to have to include your observer. So we might say he is trapped there for eternity but when the end of days comes and he passes inside it will have happened quickly , having taken zero time by his stopped clock?
Or are you saying that matter does pass the horizon and black holes do form in a short finite time but that it is unobservable from the outside?

Going back to your earlier post, my answer is YES to all those points. Yes, the falling observer would take an infinite time to reach the event horizon - in OUR reference frame. Yes, he wouild fall through very quickly, in HIS reference frame. We "see" him trapped there for eternity, ever edging closer to the EH. But he does not then fall through quickly as our clocks tick over to infinity. That is meaningless. His clock is never stopped, in either reference frame, because our clocks never "reach" infinity. It is like the old quandary "Do parallel lines never meet, or do they meet at infinity?". I'll know the answer when I get to infinity.

Mike

 

[Mike Holland]

It is, in the sense that our "now" at any given event consists of those events that are *outside* our past light cone, and also outside our future light cone.

OK, I see how you are using the word "now", to include ALL events that COULD be "now" for us, depending on our chosen coordinate system. I would have called them "indeterminate". As for the BH being there, I am still convinced that the eternally collapsing object is there, but not the BH yet.

A portion of the region inside the horizon is in our future light cone, at least as long as the BH is not close to finally evaporating; the rest of the region inside the horizon is in our "now".

I see that a portion of the BH can be in our future light cone - I could chuck something into it. But good old time dilation still comes into the picture, and just as our past light cone is distorted by the event horizon, so is our future one. The edge of my future light cone will approach the EH asymptotically (MY time frame, remember) and only reach it at t = infinity.

I don't have to invent any; there are already at least three that I know of: ingoing Painleve coordinates, ingoing Eddington-Finkelstein coordinates, and Kruskal coordinates. All of those charts embody a simultaneity convention that removes the infinity at the horizon and includes many surfaces of simultaneity that cross the horizon.

Painleve coords are based on a moving reference frame (the raindrop), and that is not MY coordinate system. They do not show the Schwarzschild coordinate system calculations for a remote observer to be false.

Look at the lines of equal Schwarzschild time in the Eddington -Finkelstein diagram, and you will see they all well up asymptotically from the event horizon in the infinite past. You will have to crossd an infinity of Schwarzschild time lines to get to the EH.

So none of these reference frames contradict calculations based on Schwarzschild coords. The only question is, what time coordinates is my wristwatch based on? V = root(r/2GM - 1)? Or those of the falling raindrop?

If you think something can fall through the event horizon in a finite time, how does it avoid the time dilation? Does it go round the back of the BH where we distant observers can't see it fall in? :)

Mike

 

[PAllen]

Mike, do you insist that seeing an Einstein ring means stars must be considered smeared into a ring by an observer that sees this? The effect BH on freezing light is physically the same phenomenon - just gravity bending or freezing light. There is no physical basis at all for interpreting this frozen light as 'reality' at all, let alone the only plausible reality for distant observers. Especially since even in SR (let alone GR) a basic understanding is that any choice of simultaneity is a pure convention, restricted only by the requirement that a surface of simultaneity be spacelike. Given this, there are uncountable infinite valid choices for simultaneity for distant observers which provide a specific time time for the formation of the event horizon and the singularity.