One of us should really go out and buy hawking’s book and quote a few passages for the sake of the rest of us to put this matter to rest.
How does energy radiate out from a black hole? Isn’t that the whole idea of a black hole, that that’s not possible?
I’m fairly certain I’m suffering from the same problem Xerxes mentions. Galo Aguirre, I did read A Brief History, and I didn’t get it then either.
At any rate, though, I also wanted to commend Chronos on a very interesting and well-written Staff report.
I also have a very simple question.
The column stated that the Sun has a Schwarzschild radius of 3km. So closer than that to the Sun, no light escapes? So if you’re standing on the Sun, what does it look like? My ‘Starry Nights’ program shows that it looks yellow and shiny, but now I’m skeptical.
Also, is there a Schwarzschild radius for the Earth? I’d do the math, but I have a liberal arts degree. I get the feeling that below a certain mass, there is no Schwarzschild radius, or the Schwarzschild radius is smaller across than an atom, or something like that. I wonder what that mass is?
Galo Aguirre and White Lightning: The gravitational field stores energy, much like an electric field. Quantum field theory says that energy can spontaneously create particles. The created particles are not virtual. For example, a gamma ray, which is a form of electromagnetic energy, can spontaneously create an electron, and it’s antiparticle - the positron. Likewise the electron and positron can annihilate each other and form a gamma ray.
Near the event horizon of a black hole, the gravitational energy density is high enough to create particle pairs in this manner, as Hawking showed. (One of his claims to fame.) Sometimes one particle falls into the black hole, but one escapes. (That conserves momentum.) Note that neither particle was ever inside the event horizon. The escaping particle carries mass, and energy, so the black hole loses the amount of mass necessary to account for that mass and the energy. Correspondingly, the gravitational field is reduced, so it all works out neatly.
Mielikki, if the sun were a black hole, then it’s event horizon would be at the Schwarzschild radius. Since most of the sun is outside of that radius, there is no black hole there. The same with the earth. There is no intrinsic mass below which you can not form a black hole. (Unless, of course, some unknown quantum gravity theory says there is.) You can do the math to figure out what mass forms an atom sized Schwarzschild radius. Take the radius to be 1 angstrom, and use that GM/c squared
formula.
I still don’t understand the static electric field that a charged black hole exerts, however.
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3 km from the center of the sun. The sun would only be a black hole if the matter was so dense that it all fit within a 3 km radius sphere. And the event horizon would occur at the 3 km point. If your mass doesn’t fit within the Schwarzschild radius, you don’t have a black hole.
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Sure, there’s a Schwarzchild radius for the Earth. Its radius would probably be measured in centimeters. You’d need to pack the Earth pretty tight for it to be a (very small) black hole.
You’ve mistaken the meaning of the Schwartzchild radius. It is the radius into which any given mass must be compressed in order to collapse into a black hole. It is also the radius of the event horizon.
So when Chronos said the sun’s Schwartzchild radius is 3 km, he was telling us that if you were to somehow mash the sun down to a ball 6000 meters in diameter, it would become a black hole. With the sun at its present size, the Schwartzchild radius has no effect.
This is the way I understand it.
According to the Hesienbergh Uncertainty Principle, you can never know the Position and Velocity of a particle. If there are particles inside the singularity, you DO know there position and velocity (the same as the singularity) Hawking Radiation compensates for this. You can not really define a particle as being anywhere, only that it has a % chance of being somewhere, a % chance of being somewhere else, a % chance of being yet another place. This is like the electrons in the electron cloud of an atom. For a black hole, some of these places the particle may be are outside the black hole, so the particle pretty much appears outside and escapes. It’s the same as the Quantum Barrier Principle (I think thats whats its called), where an electron apears to go through an un passable barrier.
Another way to think of it is that the particle speeds to a speed higher than c, crosses the Event Horizon and escapes. This is because we know where all the particles are, therefore we cannot know their velocity, so it could be faster than c.
What it REALLY comes down to is that our physics can’t say whats going on inside a Black Hole yet.
I have a question, IIRC a naked singularity is a singularity with no event horizon. Why would this destroy the universe?
To answer Mielikki’s question, just for grins, let’s figure out the mass of a black hole with an event horizon 1 Angstrom in radius. I’m doing this from old memory, and showing my work so that someone can come along and correct my errors.
Let’s see, if something is travelling in orbit, then it needs a force inwards on it which is
F = mv[sup]2[/sup]/2r
… where v is the orbital velocity, and m is the mass of the object. This is provided by gravity, which is
F = mMG/r[sup]2[/sup],
… where M is the mass of the object it’s orbiting, and G is the gravitational constant. Oh, yes, and r is the distance between the centers of the 2 objects both times. So,
mv[sup]2[/sup]/2r = mMG/r[sup]2[/sup], or
v[sup]2[/sup]r = 2MG,
… for a normal orbit. Where the event horizon comes in, is when the escape velocity is the speed of light, so that even light can’t escape, so v = c.
So, looking up a few constants on the web, in consistent units, without too much precision:
G = 6.67 * 10[sup]-8[/sup] cm[sup]3[/sup]/g * s[sup]2[/sup],
c = 3 * 10[sup]10[/sup] cm/s,
and our 1 Angstrom radius becomes
r = 1 * 10[sup]-8[/sup] cm.
M = c[sup]2[/sup]r/2G = 6.75 * 10[sup]19[/sup] g, or 6.75 * 10[sup]16[/sup] kg
The Earth has a mass of 5.98 * 10[sup]24[/sup] kg, so I suppose it would be larger than an Angstrom. Actually, we can figure that out, too:
r = 2GM/c[sup]2[/sup] = 0.886 cm, or just under a centimeter.
(I’m still not very clear on the mass leaving the black hole, though. While I see BioHazard’s post on preview, I don’t think his explanation is consistent with the original report.)
The thing with the Sun, is that the Schwarzschild radius is measured from the center of the mass, not from the surface. And you can’t get within 3 km of the center of the Sun, because you run into the surface a long time before then. If we assume that you have some amazing heat-resistant spacecraft which can fly down into the core of the Sun, then it’s still not a problem, because it’s only the mass closer to the center than you that matters, and very little of the mass of the Sun is within 3 km of the center. So the Schwarzschild radius of that amount of mass is that much smaller.
Every mass has a Schwarzschild radius, and it is quite possible for that radius to be smaller than an atom. There’s some question as to what, if anything, is the significance of, say, the S. radius of an electron, but we can calculate it (it’s an insanely small distance, even by physics standards).
As for the mechanism of Hawking radiation: Hawking spends a whole chapter on it, and I’m not sure that it’s possible to give a complete and accurate explanation of it in much less space than that (and we can’t just copy that chapter over onto the board, because it’s copyrighted). If you try to make the explanation too simple, it ends up just being wrong. The simplest non-wrong explanation I can give is this: Due to virtual particle pairs being separated, some particles manage to go from the vicinity of the black hole to great distances away. Since these particles have energy, that energy must have come from somewhere, and the only place for it to come from is the mass of the hole.
On preview, I see that others have already covered a lot of this, but I started typing a couple of hours ago, so I’ll leave it in.
That’s okay, and thanks for stopping by to say that much. I have no problem with the answer being “it’s really complicated”. In fact, that’s somewhat comforting, since it keeps me from feeling quite so ignorant for not understanding it immediately.
I shall strive to do some reading on the topic when I have time.
It may not be consistent with the original report but it is still valid. I’m pretty sure that Hawking gave an explanation like mine in that book, or another one, but it could have been a different writer.
What I said is just as valid, it describes the same thing, but any/all of the explanations are physical descriptions of what the math says, so they don’t neccesarily relate to the real universe.
I have another question. The report didn’t mention anything about Hawkings Theory that the event horizon can never decrease in size due to the Law of Increasing Entropy, it can only increase. If that theory is true, then a Black Hole would eventually explode.
All right, you can apparently grasp the notion that the one virtual particle that “got away” had a mass that had to come from somewhere, yes? And that somewhere would be the black hole.
So where’s the confusion? The other virtual particle - of the virtual particle pair - also had a mass that had to come from somewhere. That somewhere was also the black hole. It’s just that, in the case of the virtual particle that didn’t get away, that mass was almost instantly returned to the black hole, resulting in no net gain from the one “re-absorbed” virtual particle, and a net loss from the escaped virtual particle.
Yeah, but why does the thing forever remain a black hole?
I’m going to guess that as the black hole goes down in mass, it must get denser, so that you keep that high gravity.
But what would make it do that?
Or, if they don’t know that, why do they think it will stay a black hole?
Having just finished the book a few weeks ago (xmas present from Mrs. Prefect) and not being a physicist all I can do is parrot from memory and confused recollection…
<WAG>
The creation of the particle-antiparticle pair do not come from nothing, but by borrowing energy from the universe. This happens all over the cosmos all the time. Most occurrences will take place away from an event horizon and will quickly collapse upon themselves and be annihilated. However, if the energy that creates the pair of particle pairs comes from the black hole and only one particle is returned, you would have a net loss of energy. This could reduce the energy keeping the black hole from collapsing further on itself and prevent one less particle pair to form resulting in less potential mass.
</WAG>
Crap. Somehow I missed SPOOFE’s post, which was what I was trying to say.
I believe you are mistaken to assume that particles must be virtual. If my memory serves me, virtual particles can not be directly detected. There is nothing, in principle, preventing one from detecting the escaping particle.
Within General Relativity - so ignoring quantum effects - you can think of the black hole as not disappearing because the matter is no longer within the universe. You describe the universe with a set of points called a manifold. The singularity is not part of the manifold. That “point” is not part of the set. “Unsingularlizing” the black hole would be required to get rid of the black hole. So, you take mass out, the Schwarschild radius shrinks, but the black hole never goes away. Again, I’m ingnoring all things quantum, and quantum physics is necessary to make the holes lose mass, but so it goes.
I used quotes because the singularity persists in time, so it is not a point, but at least a one-dimensional object. Relying on my shakey memory, I believe the it is actually two dimensional, but that is complicated to show. (Look up the the Kruskal extension if you must.)
The confusion is that at the time when the virtual pair zapped into being, their mass didn’t come from the black hole. That’s the point - they are created outside it, so the idea that mass is ‘returned’ can’t (in my admittedly incomplete and probably mostly wrong understanding of this) be right. I could go with the idea that somehow the 2nd particle (the one that got swallowed) somehow had some property that was the inverse of the one that got away, and in that sense the cosmic ledger book is squared up, but I’ve still yet to hear an explanation which really resonates with me.
That this is my problem and not a problem with reality goes without saying, of course.
Xerxes, I think your problem is thinking of the black hole as an object made of particles. Without a quantum theory of gravity, no one really knows what a black hole is made of. According to “classical” General Relativity, which admittedly is something of an oxymoron, you can look at all of the “mass” as residing in the gravitational field. There is no “point” in the universe in which the black hole’s particles can reside. It is this incomprehensibility, caused by all sorts of 1/0 in the equations, that a quantum theory would, presumably, solve.
Quantum field theory has virtual particles popping in an out of the vacuum. This does not violate conservation of energy, because the virtual particles do not last long enough - the Heisenberg principle. This effect has actually been measured.
In the case of the black hole, the particles can hang around and become “real”, because they take energy from the black hole’s gravitational field. The energy of the field is lessened, and by the equivalence of energy and mass mentioned above, the mass of the black hole is lessened.
If you think about it, the only way you know the mass of something is either by its gravitational field, or its behavior in some other gravitational field. Fling a piece of the earth out into space. You suddenly weigh less, which you know because the gravitational pull of the earth is lessened.
It would seem the same logic would permit you to do equally well by waiting for some particles to be created out of the earth’s gravitational field and throwing them out into space. No, I really don’t understand how that works. No particles left the earth, but suddenly it weighs less. Probably looks like quantum tunneling, but I have no idea.
SlowMindThinking; Thanks!
While I might not understand how they do become real, this is the key thing I was missing.