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Black hole growth paradox 
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#1
Dec2912, 07:44 PM

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Much of what people say about the vicinity of black holes doesn't seem to make sense.
For instance, it seems to be impossible for a black hole to grow by "ingestion" by scooping up matter around it or in its path, at least in the traditional sense. Gravitational time dilation takes care of that  no particle having mass will ever reach the event horizon, much less travel through it, and because of the asymptotic partitioning of spacetime at the horizon, I don't think that even a photon can penetrate a black hole as it would have to raise itself to an infinite frequency. So an event horizon seems to be impenetrable  from either direction. However, it seems that a black hole can ingest matter by growing. If a massive object approaches a black hole, and comes close enough such that the two combined masses (or portions of a mass) now fit within their paired Schwarzschild radius, a new shelllike event horizon will form behind the intruding mass, and in the process, any other matter around the original black hole is now engulfed within the new expanded radius. For instance, if a neutron star of about two solar masses approaches a black hole containing about 60 million solar masses such that its entirety is within about 6 kilometers of the event horizon, a new event horizon will form behind it, and in the process engulf enough space to contain the volume of the Sun (if my math is correct). Thus the structure of black holes could be a series of horizon shells around the original dense core, each one partitioning its contents out of the accessible universe, but also partitioning themselves from each other. The internal structure of each shell and its contents would have the same properties as it did before the shell was formed, but would be inaccessible except by its own contents. In an another example, two black holes could be rotating around each other, but their combined mass would cause a new event horizon to form some distance away, appearing externally as a single entity, but internally, there would still be two black holes and the matter orbiting their center(s) of gravity. In the collapse of a super nova core or a neutron star > 3 solar masses, the resulting black hole does not have to form all at once, but could be a cascade of event horizons, each outer partition seeing any inner partition(s) as a black hole, and any outer partitions as infinite spacetime(?). This could solve the infinite mass paradox  "time" would take the place of the Pauli exclusion principal. As far as the oft told story that passengers in a rocket approching and entering an event horizon would never notice that they had sailed past the end of time  in years, an infinite number raised to the infinite power an infinite number of times  pretty darned unlikely I would think. Instead, one of two things might happen: 1) they could eventually be engulfed by a new event horizon and seem to appear in a new universe that they don't recognize except for nearby objects; and/or 2) if Mr. Hawking is correct, the black hole, having run out of material with which to grow, and over a vast amount of time (for a large object), might evaporate as the rocket approached it; to the passengers, it would be as if the black hole became smaller as they were about to touch it, disappearing entirely as they passed through its center  several quadrillion years in the future. Good luck finding your way home after that. If Mr. Hawking is correct, and the shell hypothesis is also correct, then we would have Hawking radiation leaking from shell to shell, greatly increasing the time it takes for a black hole to evaporate, but also providing a way for inner shells to become visible once again, either externally or internally. I think this would solve the "missing data" conundrum as well. Comments please? Chris 


#2
Dec2912, 08:09 PM

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http://www.physicsforums.com/showthread.php?t=656805 A good quick answer to your basic objection is here: http://math.ucr.edu/home/baez/physic...s/fall_in.html I would recommend reading that Usenet Physics FAQ entry before posting further. Many threads on this topic end up getting locked because people get told the correct answer repeatedly, but it's counterintuitive so they refuse to accept it. I'll respond to the main points you raise below, but you shouldn't depend just on my responses. The issues you raise, and the responses to them, have been well understood by physicists for decades. To investigate whether an object with mass can fall through the horizon, we have to look at the actual physics, not coordinates. The easiest physical quantity to look at is the proper time along the infalling object's worldline; this can be calculated, and it directly reflects the time registered on a clock following the worldline. When you calculate it, you find that it's finite: that is, an infalling clock registers a finite time elapsed to the horizon. This shows that your claim, that "no particle having mass will ever reach the event horizon", is false; such a particle *will* reach the horizon in a finite time by its own clock. 


#3
Dec3012, 10:15 AM

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I read that the schwarzschild singularity was just of coordinates but not of spacetime. However there seem to be a singularity at the origin.



#4
Dec3012, 10:28 AM

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Black hole growth paradox
Yes. The singularity at the horizon r=2M is due to bad coordinates, just as the point r=0 in spherical coordinates; the Jacobian vanishes there. A simple way to find this is to calculate curvature scalars; these are independent of the coordinates choses.
These curvature scalars will diverge for "physical singularities", indicating that EVERY observer will measure that the curvature diverges if you approach such a point. 


#5
Dec3012, 11:46 AM

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#6
Dec3012, 03:41 PM

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http://grwiki.physics.ncsu.edu/wiki/...nyder_Collapse http://en.wikipedia.org/wiki/Photon_sphere Re: speculation. It is against the forum rules to be overly speculative or to promote personal theories. This forum is for learning mainstream physics only. Please learn GR as it is, this is not the place to try to fix it. Also, take advantage of the fact that many of the experts have faced and overcome the same mental hurdles you are facing. Re: brevity. Spend some time to consider your confusion or question and find the root misunderstanding you are facing. Once you have figured that out, ask it as clearly and succinctly as possible. If you embellish or go off on tangents then you run the risk of having people who could answer your main question becoming distracted and wasting time and effort addressing your tangents and embellishments instead. 


#7
Dec3012, 04:06 PM

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Hi, Peter,
Thanks for your time and your response. Thus the structure of black holes could be a series of horizon shells around the original dense core, each one partitioning its contents out of the accessible universe, but also partitioning themselves from each other. The internal structure of each shell and its contents would have the same properties as it did before the shell was formed, but would be inaccessible except by its own contents. Again, thanks for your time. Chris 


#8
Dec3012, 05:25 PM

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#9
Dec3012, 05:28 PM

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There are many parallels between the Rindler horizon and BH horizons; in particular, external static observers must be always accelerating (however slightly) to stay static. Thus external observers are analogous to Rindler observers in SR. Also, note that static observers near a BH horizon are increasingly implausible  the force needed to maintain the static position approaches infinite. As soon as such an observer stops experiencing near infinite gforce from the acceleration, they rapidly (per their watch) cross the horizon. 


#10
Dec3012, 05:43 PM

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The key point here is that, as I said in my last post, coordinates are just numbers that label events; they don't have any intrinsic physical meaning. In particular, a coordinate labeling can be highly distorted. An example from ordinary experience is the Mercator coordinate chart, which is used to map the Earth's surface. In this chart, the coordinates of the North and South poles are infinite, but that doesn't mean the actual physical distance to the poles is infinite. The chart just becomes more and more distorted as you approach the poles, to the point of "infinite distortion" *at* the poles. Similarly, Schwarzschild coordinates become more and more distorted as you approach the horizon, to the point of "infinite distortion" *at* the horizon. So curves of finite length can "look infinite" in these coordinates at the horizon, but that doesn't mean they really are infinite. (1) Some people think it's a "paradox" that you can have black holes with different masses but singularities of "the same size" (zero size) at the center. This isn't actually a paradox, because the spacetime curvature of the hole, which is what we measure that leads us to attribute "mass" to it, is not actually coming from the singularity at the center. It's coming from the past, from the object that originally collapsed to form the hole. The Usenet Physics FAQ has a good, if brief, entry on this: http://math.ucr.edu/home/baez/physic...k_gravity.html So black holes with different masses have different spacetime curvatures, because they were formed from different collapse processes with different amounts of matter; that's what makes them different. The singularities at the center don't have to be different. (2) There is, however, an issue (at least many people, including me, think it's an issue) with the fact that the singularity at the center of a black hole has infinite density. That means it also has infinite spacetime curvature, and *that* means that mathematical quantities that tell us about the physical characteristics of spacetime become singular there. The mainstream view in GR, as I understand it, is that this tells us that GR as a theory breaks down at the singularity. Of course the big question then is, if GR breaks down at the singularity, what replaces it? This is a major reason why physicists talk about searching for a theory of quantum gravity: such a theory would be the most promising candidate to take over from GR in situations like this. Basically, the idea is that when spacetime curvature gets strong enough (the usual definition of "strong enough" is that the radius of curvature is of the order of the Planck length, 10^35 meters), quantum effects become significant, and the behavior of spacetime changespossibly to the point that "spacetime" is no longer even a good description of physics at this scale. None of this, however, affects the physics far enough away from the singularity; and for any black hole of practical interest (which means holes of stellar mass or larger), "far enough away" from the singularity is still well inside the horizon. So the issue of what the correct physics is at the singularity, while it is a genuine issue, doesn't affect any of the points under discussion in this thread. 


#11
Dec3112, 11:34 AM

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Hi, Peter,
Now add some infalling mass that goes into orbit around either the BHs or their combined center of gravity (at their LaGrange points). At some time, the orbiting mass + all (or portions of) the orbiting BHs reaches critical density around the common center of gravity. At first, this new even horizon is likely to pierce the horizons of the original BHs  would you consider this a merger?  but after more mass is accumulated, in this case, just a few hundred solar masses since the new entitity "borrows" mass from the original pair  the "central" horizon moves beyond the original BH horizons. Now what do we have? Thanks, Chris 


#12
Dec3112, 12:27 PM

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Thanks for being direct. Chris 


#13
Dec3112, 12:33 PM

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Furthermore, another BH of the same mass is not "a very small object", and you can't treat it as one. You simply can't construct a stable scenario with two BHs orbiting each other this way. Gravity in GR is nonlinear, so you can't just superpose two individual BH solutions and get another solution. That's not to say that it's impossible for two BHs to orbit each other, just that it's not as simple as just having them orbit each other like two billiard balls. In what follows, I'm going to pretend for the sake of argument that we *can* construct a stable system with two BHs orbiting each other fairly closely (but not as close as you've said). "Stable" here means the BHs stay in their mutual orbit for a long enough time compared to whatever experiments we are going to run; but it's important to note that such a system, even if it can be constructed, will *not* stay stable indefinitely. The two BHs will gradually spiral into each other because the system as a whole will be emitting gravitational waves and therefore losing energy, just as a binary pulsar system does (this has been confirmed by observation): http://en.wikipedia.org/wiki/Binary_pulsar In view of the above, please bear in mind that everything I'm saying is only heuristic; I am not working from an actual known solution of the GR equations. So this is really just handwavingeducated handwaving, I hope, but still handwaving. The strict answer would simply be that the scenario you have tried to construct is not valid; but I know that's not very satisfying, so I'm trying to do more than that, with caveats as above. Also, the event horizon doesn't "jump" from one radius to another; it moves smoothly between them. Consider a simpler case for a bit: a single black hole that gains mass from a spherically symmetric, thin shell of infalling matter. The mass of the BH plus the shell is larger than the mass of the BH by itself, so what happens when the shell reaches the new, larger horizon radius due to the combined mass (which is slightly larger than the original horizon radius)? When the shell reaches that point, the new event horizon with a larger radius must be formed, right? Yes, it is, but now consider a light ray that is moving outward, just outside the original horizon radius, in such a way that it just happens to hit the infalling shell at exactly the instant that the shell reaches the new (larger) horizon radius. That light ray will be trapped: it will stay at the new horizon radius forever (because that's what the horizon *is*, locallyit's a surface where outgoing light rays are trapped at the same radius forever). But that also means that an event just inside the path of that light ray, even though it is outside the original horizon radius, can't send light signals to infinity, so it must be part of the global black hole region. In other words, globally, the event horizon expands smoothly from the original radius to the new radius as the infalling shell approaches the new radius; at the instant the shell hits the new radius, the event horizon has just reached that new radius as well. That means that we can't know exactly where the event horizon is without knowing the entire future history of the spacetimefor example, if we ourselves were hovering just outside the original BH, before the infalling shell of matter came in, we could find ourselves stuck inside the new BH without realizing it, if we didn't know the shell was falling in, and if we were inside the new horizon radius, because the boundary of the global region that can send light signals to infinity could pass by us, moving outward, *before* we saw the infalling shell. There is no way to tell, locally, that you can no longer send light signals to infinity from your current location. This is kind of longwinded, but the point is that the event horizon is not a "thing" that you can keep track of just by looking at local phenomena. It's a globally defined boundary, and you can be misled if you try to think of it as a local thing. I realize this is not easy to visualize, and there are a lot more complications that I haven't even gone into: the infalling matter is likely to emit X rays, and as the horizons merge, gravitational waves will be emitted. There are lots of efforts ongoing to numerically simulate black hole mergers to learn more details. If you want to try to get a handle on how black holes gain mass, I would back away from the complicated scenario you've proposed, and start with the simpler case I gave above: a single, nonrotating, spherically symmetric BH that gains mass from a thin, spherically symmetric shell of infalling matter. Understanding that scenario will give a good baseline to go on to more complicated ones. 


#14
Dec3112, 12:35 PM

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#15
Dec3112, 12:37 PM

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#16
Feb113, 01:33 PM

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Peter, Your *simple* analogy is great and I understand the basics (although I will need to read alot more) of what you are saying. Can I ask what the distant observer would see in the scenario that you outlined? (Assuming the light ray is from a constant signal and that the shell of infalling matter is transparant) I assume that the distant oberver will first see the signal, then as the event horizon expands, see the frequency change (redden), and finally disappear (as it is swallowed by the expanding horizon). Is this correct? It seems at odds with the standard *frozen at the event horizon* description that one reads.
Regards, Noel. 


#17
Feb113, 02:18 PM

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This will be *before* the shell reaches the new horizon radius, so if the distant observer is also watching light emitted by the shell, he will still be able to see that light when he sees the hovering astronaut disappear (though that light, from the shell, will also have been getting more and more redshifted); then, some time after that (probably very soon, but the time lag depends on the mass of the hole), he will see the shell disappear. 


#18
Feb313, 03:08 PM

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Peter, Thanks for the reply. I have been reading around the subject to try to understand the principles ... but it is taking a lot longer than I thought it would! Oh well!
I appreciate what you are saying from the astronauts perspective (finite time ... growth of the event horizon ... etc.) and uderstand the basics, but I'm trying to understand the experience from the distant observers perspective. I appreciate that the astronaut, and his / her clock, will see time pass at the *normal* rate, but from the distant observers perspective I was under the impression that the rate at which the at which the astronaut is seen moving toward the event horizon (and the red shift of his signal) will approach infinity and so never actually (be seen to) cross the event horizon. But my reading of the previous posts is that from the perspective of the distant observer, irrespective of the astronaut fallingin or the event horizon growing, the astronaut / signals will drop behind the event horizon and disappear. But ... I'm still not certain so on with my reading! Regards, Noel. 


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