by BitWiz
PF Patron
P: 4,772
 Quote by BitWiz Much of what people say about the vicinity of black holes doesn't seem to make sense.
The main issues you are raising here have been discussed many times here. A typical recent thread:

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.

 Quote by BitWiz no particle having mass will ever reach the event horizon, much less travel through it
This is wrong. You haven't said why you believe this, but I suspect it's because you have seen that the Schwarzschild time coordinate goes to infinity at the horizon. That's true, but it doesn't mean anything physically. In GR, coordinates are just numbers that label events; they have no intrinsic physical meaning. The Schwarzschild time coordinate has a direct physical meaning only for observers that are at rest very, very far from the horizon. For things that happen close to the horizon, Schwarzschild coordinates are highly distorted (kind of like Mercator coordinates for the Earth near the poles) and don't directly reflect anything physical.

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.

 Quote by BitWiz and because of the asymptotic partitioning of space-time at the horizon
Can you be more specific about what you mean by this? I think I know, but this is an unusual way of stating it, so I'd like explicit confirmation of where you are getting this from.

 Quote by BitWiz I don't think that even a photon can penetrate a black hole as it would have to raise itself to an infinite frequency.
Same thing here; I suspect that you are attributing a meaning to the Schwarzschild time coordinate that it doesn't have. Photons can fall through the horizon just fine, and they don't get infinitely blueshifted when they do. You can calculate these things using similar math to the math you use to calculate the finite proper time for an infalling particle with mass.

 Quote by BitWiz 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.
This is not correct; a black hole has a single event horizon. When two black holes merge (which can happen), their horizons merge also, resulting in a single horizon. Similar remarks apply to your other scenarios.

 Quote by BitWiz This could solve the infinite mass paradox
What is the infinite mass paradox?

 Quote by BitWiz 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
They won't notice that they have crossed the horizon (at least, not by any observations they make locally), but crossing the horizon does not equate to "sailing past the end of time". See my comments on the Schwarzschild time coordinate not having any direct physical meaning, above.
 P: 102 I read that the schwarzschild singularity was just of coordinates but not of space-time. However there seem to be a singularity at the origin.
P: 869

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.
PF Patron
P: 4,463
 Quote by jk22 I read that the schwarzschild singularity was just of coordinates but not of space-time. However there seem to be a singularity at the origin.
The singularity at the origin is an invariant space-time singularity. The horizon is only singular in certain coordinate systems.
Mentor
P: 15,597
 Quote by BitWiz Much of what people say about the vicinity of black holes doesn't seem to make sense.
It certainly is confusing and counter-intuitive to learn, but it is logically self-consistent as well as being consistent with current evidence.

 Quote by BitWiz 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 space-time 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 shell-like 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.
You may be interested in the Oppenheimer-Snyder metric which describes the formation of an EH from a dust cloud.

http://grwiki.physics.ncsu.edu/wiki/...nyder_Collapse

 Quote by BitWiz 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.
This is pretty speculative. It doesn't seem to be in keeping with mainstream GR.

 Quote by BitWiz 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.
There are no stable orbits inside the EH. In fact, there are no stable orbits within the photon sphere, which is well outside of the EH.

http://en.wikipedia.org/wiki/Photon_sphere

Two comments: avoid speculation and be brief.

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.
PF Patron
P: 37
Hi, Peter,

 Quote by PeterDonis The main issues you are raising here have been discussed many times here. A typical recent thread: http://www.physicsforums.com/showthread.php?t=656805
I've gone through about 200 posts so far, and many seem to be on target. Thank you. I'm making an interim response now, and will follow up later.
This is an excellent link, thank you.
 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'm not looking to get myself banned. ;-) My goal is to natively understand GR, not to alter it to fit my preferences.
 The Schwarzschild time coordinate has a direct physical meaning only for observers that are at rest very, very far from the horizon. For things that happen close to the horizon, Schwarzschild coordinates are highly distorted (kind of like Mercator coordinates for the Earth near the poles) and don't directly reflect anything physical.
The problem for me is the "infinite" word. If I as an observer at a finite distance see that an object takes an infinite amount of time to approach a horizon, then it will take an infinite amount of time at any observer distance.
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.
 This is not correct; a black hole has a single event horizon. When two black holes merge (which can happen), their horizons merge also, resulting in a single horizon. Similar remarks apply to your other scenarios.
Even two BHs orbiting each other?
 What is the infinite mass paradox?
I misspoke. It's the density paradox. A point mass with undefined density. The paradox is that, under GR if the density of an object is high enough, it becomes undefined (gravity shrinks its volume to zero).

Chris
PF Patron
P: 4,772
 Quote by DaleSpam there are no stable orbits within the photon sphere, which is well outside of the EH.
A small technical point: actually there are no stable orbits inside r = 6M. The photon sphere is at r = 3M (and the horizon is at r = 2M); photons can orbit the hole at the photon sphere, but such orbits are unstable; small perturbations will cause an orbiting photon to either spiral into the hole or escape to infinity. The same goes for orbits of timelike objects between r = 3M and r = 6M.
PF Patron
P: 4,463
 Quote by BitWiz The problem for me is the "infinite" word. If I as an observer at a finite distance see that an object takes an infinite amount of time to approach a horizon, then it will take an infinite amount of time at any observer distance.
This is false, and is shown in pure special relativity. A uniformly accelerating rocket sees a horizon form behind it, and objects fail to reach it in infinite time, as observed by the rocket (as long as it continues to uniformly accelerate). Meanwhile, the non-accelerating objects know nothing of this horizon and 'fall' through it in finite time. Look up Rindler Horizon.

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 g-force from the acceleration, they rapidly (per their watch) cross the horizon.
PF Patron
P: 4,772
 Quote by BitWiz I'm not looking to get myself banned. ;-) My goal is to natively understand GR, not to alter it to fit my preferences.
Ok, good. For future reference, the tone of your first post in this thread did not convey that impression. I realize that it's hard to know people's expectations when you're new to a forum.

 Quote by BitWiz The problem for me is the "infinite" word. If I as an observer at a finite distance see that an object takes an infinite amount of time to approach a horizon
But you don't see that. You see that there is a *coordinate* that goes to infinity at the horizon, but that's not the same as the object actually taking an infinite amount of time to reach the horizon. The actual time experienced by the object is finite, as I said in my last post.

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.

 Quote by BitWiz Even two BHs orbiting each other?
Two BHs orbiting each other are still separate BHs, so they have separate event horizons; but if they merge, they merge into a single BH with a single event horizon.

 Quote by BitWiz The paradox is that, under GR if the density of an object is high enough, it becomes undefined (gravity shrinks its volume to zero).
Ok, that clears things up a bit. There are really two issues here:

(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 changes--possibly 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.
PF Patron
P: 37
Hi, Peter,
 Quote by PeterDonis Two BHs orbiting each other are still separate BHs, so they have separate event horizons; but if they merge, they merge into a single BH with a single event horizon.
Let's worst-case this. Let's say I have two black holes with a combined mass of 1000 solar masses orbiting (really fast) at 3500 km separation, and for the sake of simplicity, that their event horizons remain roughly spherical. I thus have two separate BHs and two horizons.

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
PF Patron
P: 37
 Quote by PeterDonis Ok, good. For future reference, the tone of your first post in this thread did not convey that impression. I realize that it's hard to know people's expectations when you're new to a forum.
Thanks, Peter. I'm more engineer than scientist, more logician than math, so I'm probably more like a foreigner than "new," but I will learn to get along. My specialty is systems, and I want to understand GR as a system. That seems to be an uncommon approach; or perhaps I'm in the wrong forum.

Thanks for being direct.

Chris
PF Patron
P: 4,772
 Quote by BitWiz Let's say I have two black holes with a combined mass of 1000 solar masses orbiting (really fast) at 3500 km separation, and for the sake of simplicity, that their event horizons remain roughly spherical. I thus have two separate BHs and two horizons.
I see your intent here, but it won't work as you've described it. Your intent appears to be to have the horizons separated by a very small distance, but there is no way to have such a configuration be stable. As I posted earlier in this thread, there are no stable orbits inside r = 6M, which is three times the horizon radius; so even a very small object can't orbit the BH just outside its horizon.

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 handwaving--educated 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.

 Quote by BitWiz 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.
Yes, but that doesn't mean an event horizon instantaneously forms there. An event horizon is a globally defined surface: it's the boundary of a region of spacetime (a "black hole") that can't send light signals to infinity. If two black holes are merging, then there is really only one event horizon; it just has two "branches" in the past instead of a single one. But since the final configuration is a single black hole, there is only one region of spacetime as a whole that can't send light signals to infinity; again, that region just has two "branches" instead of one, so if you drew a spacetime diagram, for instance, with time vertical and spatial dimensions horizontal, the black hole region would look like a pair of trousers, so to speak, instead of a cylinder.

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*, locally--it'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 spacetime--for 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 long-winded, 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.

 Quote by BitWiz At first, this new even horizon is likely to pierce the horizons of the original BHs
No. What will happen is that the event horizons of the two original BHs will start expanding, *before* the new matter has accumulated; they will probably merge with each other even before all the new matter has fallen in, and then the single combined EH will continue to expand until all of the accumulating matter has fallen inside the new horizon radius due to the final total mass present. After everything is all done, there will be a single BH, and a single event horizon.

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, non-rotating, 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.
PF Patron
P: 4,772
 Quote by BitWiz I'm more engineer than scientist, more logician than math, so I'm probably more like a foreigner than "new," but I will learn to get along. My specialty is systems, and I want to understand GR as a system. That seems to be an uncommon approach; or perhaps I'm in the wrong forum.
The questions you're asking are appropriate for this forum, and they're good questions.
PF Patron
P: 4,772
 Quote by PeterDonis 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, non-rotating, spherically symmetric BH that gains mass from a thin, spherically symmetric shell of infalling matter.
Btw, a very good, readable popular book on GR that discusses this type of scenario is Kip Thorne's Black Holes and Time Warps. I would highly recommend it if you want a reasonably non-technical description of the kinds of things I've been talking about here.
 P: 259 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.
PF Patron