Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: chris on 05/09/2014 09:05:55
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When a black hole forms and subsequently accretes matter, what happens to the material that is consumed? Is the fate of a black hole to relentlessly and indefinitely grow, assuming there is an endless supply of material with which to feed it?
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When a black hole forms and subsequently accretes matter, what happens to the material that is consumed?
There are conflicting opinions about this. Most textbooks will tell you that material falls through the event horizon of a large black hole without incident, then reaches a central point-singularity in finite proper time where it is destroyed. However if you look at Kevin Brown's formation and growth of black holes (http://mathpages.com/rr/s7-02/7-02.htm) you can also see mention of Oppenheimer's original "frozen star" interpretation. Kevin Brown doesn't favour it, but he doesn't totally write it off. It's where the infalling material effectively freezes at the event horizon due to the infinite gravitational time dilation. The black hole grows something like a hailstone. Imagine you're a water molecule. You alight upon a growing hailstone. You can't pass through the surface, but other water molecules surround you and bury you. So whilst you can't pass through the surface, the surface can pass through you. So you end up on the wrong side of the event horizon.
If you look around a bit further you can dig up the gravastar (http://en.wikipedia.org/wiki/Gravastar) which features "a void in the fabric of space and time". This is described as an alternative to the black hole, but it's just about the same as the original frozen star. And IMHO that void makes it even more of a hole than the traditional black hole. Look at the image on the Wiki Hawking radiation (http://en.wikipedia.org/wiki/Hawking_radiation) article. Imagine a hole in space.
When you cast the net even wider you find Friedwardt Winterberg's firewall, see the abstract here (http://www.znaturforsch.com/aa/v56a/56a0889.pdf). This says the infalling material is destroyed before it even gets to the event horizon. Atoms and electrons etc are ripped apart and converted into gamma radiation (and I presume neutrinos) on the way in, some of which escapes. This firewall predates the AMPS firewall (http://en.wikipedia.org/wiki/Firewall_(physics)), and was referenced in http://arxiv.org/abs/1304.6483. I actually think it's right myself, and don't quite understand why it isn't better known.
Is the fate of a black hole to relentlessly and indefinitely grow, assuming there is an endless supply of material with which to feed it?
As far as I know, yes. There is of course Hawking radiation (http://en.wikipedia.org/wiki/Hawking_radiation), which people rather take for granted. But it remains hypothetical. As does Hawking's recent there are no black holes (http://www.nature.com/news/stephen-hawking-there-are-no-black-holes-1.14583) conjecture. But for myself I'm happy that there are some very small very massive things out there that are as black as the ace of spades, and they aren't going anywhere any time soon.
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Cosmologists suggest that after a black hole has absorbed the nearby surrounding matter in its galaxy, and merged with any black holes from nearby galaxies (due to gravitational radiation), they will sit there absorbing any remaining light and cosmic background radiation that is left.
The (accelerating) general expansion of the universe will ensure that distant black holes are carried far apart, until there is nothing left to consume.
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There's no need for anything to 'freeze' anywhere. Defined locally time stops for noone. It's actually a very Ptolemaic assumption to use only one clock and ruler to define a universe from. To do so should also invalidate relativity.
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As for what will happen to a universe consisting of super massive black holes at the galaxy centers? Depends on how super massive they are I think, 'gravity's reach' sort of? Including a accelerating expansion naturally. Maybe each galaxy will contract into a super massive center? Assuming a endless feeding of matter (mass) it should be whatever distance versus that mass that decides it.
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There's no need for anything to 'freeze' anywhere. Defined locally time stops for noone. It's actually a very Ptolemaic assumption to use only one clock and ruler to define a universe from. To do so should also invalidate relativity.
That's what you generally read, but see this in Kevin Brown's article (http://mathpages.com/rr/s7-02/7-02.htm):
"Incidentally, I should probably qualify my dismissal of the 'frozen star' interpretation, because there's a sense in which it's valid, or at least defensible. Remember that historically the two most common conceptual models for general relativity have been the "geometric interpretation" (as originally conceived by Einstein) and the "field interpretation" (patterned after the quantum field theories of the other fundamental interactions). These two views are operationally equivalent outside event horizons, but they tend to lead to different conceptions of the limit of gravitational collapse. According to the field interpretation, a clock runs increasingly slowly as it approaches the event horizon (due to the strength of the field), and the natural "limit" of this process is that the clock just asymptotically approaches "full stop" (i.e., running at a rate of zero) as it approaches the horizon. It continues to exist for the rest of time, but it's "frozen" due to the strength of the gravitational field. Within this conceptual framework there's nothing more to be said about the clock's existence. This leads to the "frozen star" conception of gravitational collapse."
I can't fault that myself. But Kevin Brown goes on to say this:
"In contrast, according to the geometric interpretation, all clocks run at the same rate, measuring out real distances along worldlines in spacetime. This leads us to think that, rather than slowing down as it approaches the event horizon, the clock is following a shorter and shorter path to the future. In fact, the path gets shorter at such a rate that it actually reaches (our) future infinity in finite proper time."
Our future infinity? That's saying the infalling body reaches the central point-singularity at the end of time. So it hasn't reached it yet. The finite proper time is still occurring, and always will be. I conclude that Kruskal-Szekeres coordinates are effectively putting a stopped observer in front of a stopped clock, and then claiming he sees it ticking normally. But it's stopped. He can't see it ticking normally. He's stopped too. So he can't see anything. Ever.
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the clock is following a shorter and shorter path to the future. In fact, the path gets shorter at such a rate that it actually reaches (our) future infinity in finite proper time
I think that perhaps this description has reversed the clocks, and has (wrongly) produced "our future infinity" time when it should have produced a "near-zero time" for the infalling clock.
My reasoning is as follows: Assume we have:-
1. an observer well away from the black hole (who has some understanding of relativity)
2. an observer falling directly towards a block hole (ie not orbiting around it)
3. Both observers have a local clock
4. Both observers are linked by a laser beam which continually transmits the reading of his local clock. Measuring the frequency of this beam allows red shift to be measured.
Observer (1) will see observer (2) falling towards the black hole at a speed which rapidly increases to a fair fraction of the speed of light. Observer (2) extrapolates the speed of observer (1) to predict that observer (1) will hit the event horizon in (say) 10 minutes by the clock of observer (2).
Observer (1) will never actually see observer (2) cross the event horizon, but will see observer (1) reach a point where his laser beam is red-shifted into undetectability.
On the other hand, observer (2) will measure this "same" time as well under 10 minutes, due to gravitational time dilation; the most extreme time dilation ocurring in the last minute and the last second.
So rather than observer (2) seeing the infinite future of observer (1), I expect that he will see only 10 minutes of the future of observer (1); the last minute of this period taking considerably less than a minute by the clock of observer (2).
Predicting the clock of observer (2) after he crosses the event horizon is the source of a variety of theories; whatever it is, we know of no way that observer (2) can inform observer (1) about it, so it must remain a topic of speculation.
[What I can't work out is whether observer (2) will see the laser from observer (1) will be red-shifted, blue shifted or unchanged as observer (2) approaches the event horizon; I guess it all depends on the orbit of observer (1) compared to the falling trajectory of observer (2).]
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He's playing with concepts and words there. Nothing difficult about a proper time, and we know it exist, if it didn't we would all be timeless :). You can define it any way you like, choosing appropriate coordinates, but when doing so one has to remember not to presume those coordinates to be in any way special. There is no gold standard for a clock, except the one expressed through Lorentz transformations. That they exist, and work, prove the reality of local constants making sense, and also gives us yet another definition in where as you say, we might define a, theoretical, gold standard. That gold standard though to me discuss logics, and whether there is a underlying logic to physics, astronomy, chemistry etc, etc. Finding Lorentz transformations giving us a comprehensive framework, describing this seamlessly existing four dimensional universe we define ourselves inside, we have one description in where we all exist, the other is then those clocks and rulers we define versus each other. There you have constants origin too. They are found to exist no matter where you are, measuring them. So locality is not the exact same as this seamlessly existing universe we describe for each other, but locality is the origin of a logic that also can be applied to a 'whole universe'.
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I should also point out that assuming constants to be found, and applicable, through a universe actually prove the concept of those local clocks all being , in a slightly weird sense, equivalent. You have to think this through to see in what sense they should be equivalent though. It all goes back to logics making the most sense, then following it.
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the clock is following a shorter and shorter path to the future. In fact, the path gets shorter at such a rate that it actually reaches (our) future infinity in finite proper time
I think that perhaps this description has reversed the clocks, and has (wrongly) produced "our future infinity" time when it should have produced a "near-zero time" for the infalling clock.
It's a fairly standard description, you can find similar descriptions elsewhere.
My reasoning is as follows: Assume we have:-
1. an observer well away from the black hole (who has some understanding of relativity)
2. an observer falling directly towards a block hole (ie not orbiting around it)
3. Both observers have a local clock
4. Both observers are linked by a laser beam which continually transmits the reading of his local clock. Measuring the frequency of this beam allows red shift to be measured.
Observer (1) will see observer (2) falling towards the black hole at a speed which rapidly increases to a fair fraction of the speed of light.
No problem with that.
Observer (2) extrapolates the speed of observer (1) to predict that observer (1) will hit the event horizon in (say) 10 minutes by the clock of observer (2).
There's maybe a mixup between 1 and 2 here.
Observer (1) will never actually see observer (2) cross the event horizon, but will see observer (1) reach a point where his laser beam is red-shifted into undetectability.
That's fair enough.
On the other hand, observer (2) will measure this "same" time as well under 10 minutes, due to gravitational time dilation; the most extreme time dilation ocurring in the last minute and the last second.
The point is this: he hasn't measured it yet, and he never ever will.
So rather than observer (2) seeing the infinite future of observer (1), I expect that he will see only 10 minutes of the future of observer (1); the last minute of this period taking considerably less than a minute by the clock of observer (2).
But observer 2 is subject to extreme time dilation. Work it through without any falling or event horizon, but with an observer 2 who is in a gendanken time-dilation chamber. The time dilation is increasing, and will shortly be infinite.
Predicting the clock of observer (2) after he crosses the event horizon is the source of a variety of theories; whatever it is, we know of no way that observer (2) can inform observer (1) about it, so it must remain a topic of speculation.
Whether he actually crosses the event horizon is the source of a variety of theories!
What I can't work out is whether observer (2) will see the laser from observer (1) will be red-shifted, blue shifted or unchanged as observer (2) approaches the event horizon; I guess it all depends on the orbit of observer (1) compared to the falling trajectory of observer (2).]
Again, work it through with just the time dilation, IMHO it becomes clearer.
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As light is trapped at the horizon it has to slow down proportionally along with the in-falling observer. Will the external observer still see the same stream of photons at the same rate? Or will those photons have to reach superluminal speeds to make this happen. If they slow down considerably at the horizon then in relation to the external observer, who can't determine this for himself physically but only mathematically, they are traveling at a significantly small fraction of c. This is why the in-falling object appears to slow down. As the stream of photons is now less dense because of the dilation the image of the in-falling object becomes ever more faint until it is then undetectable. Do they math and you will see this. Everything approaching the event horizon disappears from view.
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So what happens to the energy in the photons that are captured by a black hole? Is this converted into mass and hence contributes to the black holes gravitational field?
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It is difficult to understand radiation does escape through the z plane (jets) it would make life a lot simpler if two black holes destroyed each other and one was left with EM radiadtion only.
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When a black hole forms and subsequently accretes matter, what happens to the material that is consumed? Is the fate of a black hole to relentlessly and indefinitely grow, assuming there is an endless supply of material with which to feed it?
I recall something about small black holes exploding. When they loose too much energy from Hawking radiation and what mass left over is more than the Schwarzschild mass then there will be an outburst of matter.
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So what happens to the energy in the photons that are captured by a black hole? Is this converted into mass and hence contributes to the black holes gravitational field?
That is undetermined. Inside the black hole no one knows exactly what happens. How could you ever develop a falsifiable theory?
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The light entering has energy, which will be added to the black hole. So perhaps it imparts some momentum and makes the black hole move a little bit?
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The light entering has energy, which will be added to the black hole. So perhaps it imparts some momentum and makes the black hole move a little bit?
Most people would agree with that, but actually, it isn't cut and dried. The coordinate speed of light is said to be zero at the event horizon. How can something with a zero speed as measured from afar impart any momentum?
So what happens to the energy in the photons that are captured by a black hole? Is this converted into mass and hence contributes to the black holes gravitational field?
It's perhaps better to say the energy-momentum is exhibited as mass. The simplest example of this is the photon in the box. When you capture a massless photon in a mirror-box, it increases the mass of that system. See Einstein's E=mc² paper (https://www.fourmilab.ch/etexts/einstein/E_mc2/www/): the mass of a body is a measure of its energy-content. When you open the box, it's a radiating body losing mass. Think of photon momentum as resistance to change-in-motion for a wave propagating linearly at c. Then think of mass as resistance to change-in-motion for a wave going back and forth at c. It's like inertia is the flip side of momentum.
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Sure Chris, locally defined 'c' will be 'c', and light has a momentum. I'm guessing you're thinking of a super massive Black Hole, 'warping' space and light paths around and into it? Then again, I agree with Jeffrey. I don't know a way to define what happens once past the event horizon either? Doesn't mean that you can't speculate
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As for using 'coordinate speeds' to define what one see, one way we do that is for example when we use ones local clock and ruler to define another frame of reference from. That one I see as a result of us thinking both of this 'seamless universe', containing us all equally, then presuming that my definition should be yours too. It's a lot easier to use a local definition , which also fit the idea of physics being equivalent throughout a whole universe. In the local we can define both constants and rules, using coordinate will give each observer a unique definition of this universe, including that lump of radioactivity drifting through space. Everything, in a manner, 'observe' a universe as I think of it, as in 'interacts' with it. Each time you define somethings speed or time it will be a result of a interaction with something, another 'frame of reference' interacting with your local definition.
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better clarify this I suspect :)
We all have archetypes, one is this seamless universe we all exist in. local definitions goes out from you using your wristwatch and ruler to measure on somewhere else, another frame of reference as it is called. When you collect a lot of local measurements, from different observers being at different uniform motion you then will find a plethora of differing results. In that manner we can discuss a local measurement as being a result of your coordinates (your coordinate system, relative whatever you measure).
But what we also find doing those local measurements is that we have locally equivalent constants. and in that local measurement we all can agree on that light has a certain speed for example, all of it according to ones own clock and ruler, and that is true even though, when we measuring on other frames define their clocks and rulers as differing from our own local standard.
Either you think constants exist, and use them to define this universe, or you don't?
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A good argument for constants existing I find the idea of three objects at different uniform motion, measuring one other. None of them should agree with the others measurements, ideally that is :) but all of them should agree on that lights speed in a vacuum is the same, locally measured.
Further each one of 'B' and 'C' should give a different time and speed to 'A', which in its turn will do the same for the others. Using logic I don't find it appropriate to define 'A' speed as being of two values 'simultaneously', but that will be the result. And that is coordinate speeds. (Actually you can apply this on the 'time/clock' 'B' and 'C' will measure 'A'' to have too. They shouldn't be able to agree on it unless using a Lorentz transformation as I gather.)
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You don't need to agree on a time, or speed to get to a logic, but I do expect us to need causality. Without causality it would be a very different universe, and rather difficult to explain.