How do black holes grow?

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

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

PAllen

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The event horizon is a place where the metric tensor contains an infinity.
False. It is a place where this happens in one coordinate system that is ill fitted to this region. In other coordinates this does not happen. On the other hand, even these coordinates you can show that curvature is finite at the EH.
Thus, there are no null geodesics (light paths) that cross this "line".
False again. There are interior and exterior SC coordinates. Using these, holding theta,phi constant, you compute proper time along a radial free fall geodesic from both sides. You get finite time to reach the EH, in the limit; you get finite time to the singularity in the continuation. In other coordinates, you don't even need to do this - it is just one continuous line.
This gets quite sticky, as infinities pose a whole host of mathematical problems that most physicists just choose to ignore (not all).
The infinities at the EH are a coordinate artifact. This is routine differential geometry. Unlike QFT which has pure math problems with its foundations, differential geometry is completely rigorous, and GR is expressed in terms of differential geometry.
I am of the opinion that any final theory that integrates quantum mechanics will resolve this issue. There is likely a form of quantum tunneling that occurs once particles get close enough to the event horizon that allows them to make their way in (an, in essence, out) of the black hole in a finite time as observed from us on the outside.
That is probably true, but doesn't justify making false statements about the classical theory.
That said, if you stick strictly to only GR, the outside observer will never "see" the particle cross the event horizon. Information, in all forms, cannot escape from the inside of the BH, be it light or any other effect. Like other people have noted however, the total gravity experienced by the outside observer changes immediately after the particle falls between the observer and the BH anyway. Thus, the only information an outside observer could actually "see" happened long before the particle gets to the event horizon.
That's also fine.
 
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False. It is a place where this happens in one coordinate system that is ill fitted to this region. In other coordinates this does not happen. On the other hand, even these coordinates you can show that curvature is finite at the EH.
Yes, it happens in one particular coordinate system. I never said it happened in all coordinate systems. This particular coordinate system is used, however, to show what the event horizon is and to do an easy calculation for it. It is HARDLY just an "artifact".

False again. There are interior and exterior SC coordinates. Using these, holding theta,phi constant, you compute proper time along a radial free fall geodesic from both sides. You get finite time to reach the EH, in the limit; you get finite time to the singularity in the continuation. In other coordinates, you don't even need to do this - it is just one continuous line.
Fair enough, but I think it is important to people trying to learn this stuff to realize that what you are doing is a bit of a mathematical trick. The trick is entirely valid, and the difficulty comes in peoples minds when they attempt to reconcile the meaning behind the math. A coordinate system is just a mathematical choice, and in the end people need to think about these things in a more geometrical way, but certain coordinate systems are tied to reference frames, and so have a physical meaning. As such, per the original poster's question, there are really only two coordinate systems we can use that tie directly to the experience being asked about: the one that follows the falling object into the BH, and the one of an external observer (certain assumptions made for simplicity).

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

The infinities at the EH are a coordinate artifact. This is routine differential geometry. Unlike QFT which has pure math problems with its foundations, differential geometry is completely rigorous, and GR is expressed in terms of differential geometry.
Calling something that is highly physically important and the center of the whole issue here a simple "artifact" if ridiculous and misleading. Just because you can make a coordinate shift to push out the "crinkle" doesn't mean it isn't there. You've just hidden it inside your coordinate map. To point, the observer falling into the BH might not experience a "horizon" directly but WILL see some weird effects from the outside world as they close in on that line. The line is still there, it's still relevant, it just expresses itself differently because we are in a different coordinate system.

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

PAllen

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

Infinities are stubborn little things. They can be moved around, twisted and manipulated, but rarely can you ever make them go away.
I believe this is mathematically and conceptually invalid. The event horizon is not an artifact. However, there are no geometric discontinuities there, of any kind. All infinities there (rather than at the true singularity) are pure coordinate artifacts. Infinities from coordinate artifacts can occur anywhere. It just happens the for one coordinate system, coordinate infinities happen at the horizon.

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

NOTE: I do not say the EH is an artifact. I say any infinities there are an artifact of coordinates ill fitting for this region.
 
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Infinities are stubborn little things. They can be moved around, twisted and manipulated, but rarely can you ever make them go away.
Well, then the horizon of a black hole is one of those rare cases; you *can* make the infinity go away, completely, by using a better coordinate chart, and you can prove that all geometric invariants, i.e., all physically meaningful quantities, are finite and well-behaved at the horizon. This is a homework exercise in every GR textbook I'm aware of. It is not at all controversial.
 
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Arindamsinha, I had almost the same discussion in my topic "Black Holes - The Two Points of View" a few months back. I agree with your point of view, but have added a few provisos.

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

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

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



Mike
 
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Mike, I don't know of ANY standard coordinate system which uses the past light cone to define surfaces of simultaneity. Can you provide a mainstream reference for one?
 
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Arindamsinha, I had almost the same discussion in my topic "Black Holes - The Two Points of View" a few months back. I agree with your point of view, but have added a few provisos. [..]
Hi Mike, I saw some of that discussion, but most of it I could not follow - it was too abstract for me. I hope to be able to incite people to follow Einstein's example and discuss physical "clocks and rods". :tongue2:
A lot of the problem centers around how you define "existence" and "now". Effectively, we live at the point of our past light cone. The light we receive from the universe around us defines our "now". We see the sun "now", but are actually seeing the light that left it 8 minutes ago. And similarly for the stars and galaxies. So when we say that Sirius exists, for example, we are really saying it existed 10 years ago. [..] Similarly with "existence". [..]
Please don't include me in "we"! :surprised I mean with "now" and "exists" the same as "simultaneous" according to convention.

Note: PAllen started a topic about simultaneity.
 
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Mike, I don't know of ANY standard coordinate system which uses the past light cone to define surfaces of simultaneity. Can you provide a mainstream reference for one?
I am referring to the coordinate system we use all the time in our everyday lives. We observe a supernova, and say that it occurred in 2012. In this everyday sense it was simultaneous with our calendars reading 2012. But as it is 1000 LY away, we calculate that it "really" occurred in 1012. Someone passing by at 0.83c might say it is 500 LY away, and occurred in 1512.

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

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

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

Mike
 
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I am referring to the coordinate system we use all the time in our everyday lives.
I am asking for a scientific reference. If you don't have one, then you should stop speculating. Everyday usage is not the same as scientific usage.
 
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Sorry Dalespam, I was editing my post as you replied, and added the last comment wehich I think covers that objection.

Mike
 
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He never once defines the past light cone as a surface of simultaneity. Post a reference that actually supports your idea of "using our past light cones as our definition of 'now'", or stop speculating.
 
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If you reread my post, I did not anywhere say that my past light cone defines simultaneity for me. Obviously, and as I pointed out in my post, things that appear simultaneous but are at different distances from me are not simultaneous.

What I am saying about that past light cone is that it contains events which are in my past and can have a causal effect on me. Everything outside that cone is theoretical for me. I "assume" that the sun is still there, although I have not seen it for 8 minutes. So all these outside events may be in my future, but some of them may never enter my past light cone and never occur for me, such as black holes forming (unless I jump into one). In this sense, the light cone is my "now", with the past inside it and the future outside.

Mike
 

PAllen

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Sorry Dalespam, I was editing my post as you replied, and added the last comment wehich I think covers that objection.

Mike
In case it isn't clear, what Dalespam is complaining about is that while there simultaneity is very much a matter of convention, it is universally accepted that the one restriction is that you don't consider causally connected events to be simultaneous. You have to pick between your forward and backward light cones. Einstein's convention basically takes exactly half way between for SR.
 
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If you reread my post, I did not anywhere say that my past light cone defines simultaneity for me.
Yes, you did:
The result is that using our past light cones as our definition of "now", we can correctly say ...
And you repeat it here:
In this sense, the light cone is my "now", with the past inside it and the future outside.

The "sense" you are talking about is causality, and identifying causality with "now" is defining the past light cone as your surface of simultaneity. Not only did you say what I claimed you said, you repeated it and said it very clearly with lots of detail (but without any references).
 
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My past light cone defines simultaneous only in the sense that it defines what light signals arrive at my eye simultaneously. It does not mean that these light signals are from events that occurred simultaneously, but only that I SEE them simultaneously.

Due to the limit of the velocity of light, only events within my light cone can affect me in any way. So all photons emitted from all over the universe that arrive at my eye this instant have been emitted just as my light cone advanced to coincide with them. This defines my causal "now" without anything being simultaneous, except the arrivals at my retina.

Mike
 
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My past light cone defines simultaneous only in the sense that it defines what light signals arrive at my eye simultaneously. It does not mean that these light signals are from events that occurred simultaneously, but only that I SEE them simultaneously.
That is causality, not simultaneity. Stop trying to confound the two concepts. There is no scientific justification for doing so, and I think that you are well aware of that fact.
 
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Dalespam, I am not confounding the two. I have never claimed that they are the same. PLEASE read my posts and stop responding to what you THINK I have posted.

In the bit of my post that you quoted, I agree. When light from events reaches me, then those events can have a causal effect on me. Something that happened 10 LY away 10 years ago, and something than happened 5 LY away 5 years ago, will be on the same light cone and will be able to affect me (I will see them) at the same time. The only simultaniety is the effects arriving at me at the point of my light cone.

Do you not agree that all the photons I am seeing NOW from my present light cone arrived in my eye SIMULTANEOUSLY? And that consequently all the events on that light cone became able to affect me at the same moment? The only thing that is simultaneous is what happens here where I am. These events would not be simultaneous for anyone else.

NB Is there a word 'simultaniety'? Have I spelled it correctly? Simultaneousness??

Mike
 
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Do you not agree that all the photons I am seeing NOW from my present light cone arrived in my eye SIMULTANEOUSLY?
This is not the standard sense of the word "simultaneous" in relativity. "Simultaneous" does not apply to things that all happen at the same point in spacetime; and all the photons you are seeing NOW are arriving at your eye at the same point in spacetime. "Simultaneous" is a term standardly used in relativity to describe events that are spatially separated, and no two events that are simultaneous in the standard sense can be causally connected; the events on your past light cone are *not* simultaneous in the standard sense.

So, for example, the event on the Sun's surface at which a photon was emitted that is just striking your eye NOW--call this event E--is *not* simultaneous with the event of your seeing it--call this event S. Event E is in the causal past of event S. But an event on the Sun's surface to the future of event E could be simultaneous with event S, depending on what simultaneity convention you adopt. By the most natural such convention for us here on Earth, the event on the Sun's surface that is simultaneous with event S would be 500 seconds to the future of event E (because 500 seconds is the light travel time, in the Earth's rest frame, from the Sun to the Earth). But other conventions are possible.
 
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Dalespam, I am not confounding the two. I have never claimed that they are the same.
Yes, you are confounding they two. You are deliberately using terminology for simultaneity, most notably the word "now", to describe causality, thereby mixing up the two separate concepts and potentially causing confusion. That is what "confounding" means.

My original objection was to your "definition of 'now'" comment, which explicitly identifies the past light cone with a simultaneity convention. You even called it a coordinate system, further emphasizing the simultaneity.

I am not distorting your statements. Nobody besides you abuses the terminology this way, as your inability to provide references shows.
 
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Yes, Peter, I understand that. But I am accused of claiming that events on my light cone are simultaneous, and I have never claimed any such silly thing.

Of course events that occur at the same time and place are simultaneous, and this is so obvious that no-one bothers to discuss it. Thats why the scientists only discuss it for spatially separated events, in which case it all depends on the reference frame.

Mike
 
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Yes, Peter, I understand that. But I am accused of claiming that events on my light cone are simultaneous, and I have never claimed any such silly thing.
If you didn't intend to make such a claim, then DaleSpam is not the only one who finds your use of language to be, at the very least, confusing. I do as well.

Of course events that occur at the same time and place are simultaneous, and this is so obvious that no-one bothers to discuss it. Thats why the scientists only discuss it for spatially separated events, in which case it all depends on the reference frame.
It's good that you recognize that, but it wasn't obvious from your prior posts. Let me suggest a better way of wording what I think you may be trying to say:

The past light cone of the event "here and now" defines one *boundary* of our "now"; only events to the future of that boundary are candidates to be considered as part of our "now" (which specific events outside the boundary count as our "now" depends on the simultaneity convention we adopt). Similarly, the future light cone of the event "here and now" defines the other boundary of our "now"; only events to the past of that boundary are candidates to be considered as part of our "now". The standard Einstein simultaneity convention picks the set of events that are exactly "halfway between" these two boundaries as "now", but other conventions are possible, as long as they are consistent with the boundary requirements above.
 
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I am referring to the coordinate system we use all the time in our everyday lives. We observe a supernova, and say that it occurred in 2012. In this everyday sense it was simultaneous with our calendars reading 2012. But as it is 1000 LY away, we calculate that it "really" occurred in 1012. Someone passing by at 0.83c might say it is 500 LY away, and occurred in 1512. [..]
Ah, that's a little different. Some people may mean with "supernova" the phenomenon as seen on Earth, and which we ascribe to something that happened a long time ago. In scientific discussions we only say that Sirius exists because we know of no reason to assume that something happened to it during the last 10 years; we don't mean with "Sirius exists" that we observe it now.

However, the confusion between the time of observation here and the time of occurrence there is itself a recurring phenomenon in recent discussions; hopefully it will be settled in the thread on simultaneity.
 
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In case it isn't clear, what Dalespam is complaining about is that while there simultaneity is very much a matter of convention, it is universally accepted that the one restriction is that you don't consider causally connected events to be simultaneous. You have to pick between your forward and backward light cones. Einstein's convention basically takes exactly half way between for SR.
As a side issue, this is also why I am not happy with PeterDonis referring to the whole region between light cones as "now". All events there are certainly candidates for "now", but you need to select them by selecting a coordinate system to describe this region which you cannot view. I cannot accept the idea of causally connected events there all being referred to as "now". Not for one particular observer, anyway.

But this isn't physics. It is just the use of language.

Mike
 
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As a side issue, this is also why I am not happy with PeterDonis referring to the whole region between light cones as "now".
I actually did make an argument along those lines once, but it wasn't in this thread. For this discussion I agree that "now" refers to a particular surface of simultaneity, not to the entire region between the light cones.

I cannot accept the idea of causally connected events there all being referred to as "now".
This is a good point which I hadn't considered when I made the comments in the earlier thread I referred to above. One requirement of any reasonable concept of "now" should be that no two events in the set we label "now" can be causally connected. That makes it untenable to view the entire set of events between the light cones as "now". None of the events in that set are causally connected to the event "here and now", but there are certainly events in that set which are causally connected to each other.
 

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