View Full Version : Black holes, atoms, and infinite density

CookingWithGas

11-15-2010, 05:30 PM

At the core of a black hole is a singularity, with infinite density. I can cope with the concept, but don't understand how it's achieved.

A black hole must initially form by gravitational collapse of a pile of matter, which consists of atoms, molecules, or perhaps disembodied particles. Suppose that the gravitational pull compresses those particles down to closest-packed configuration, with effectively no space between. That's awfully damn dense, but it's not infinite. Now how do you get to anything denser? Are particles compressible? Is there some phenomenon by which more than one particle can occupy the same space? What occurs in a black hole that is different than a neutron star?

SmithCommaJohn

11-15-2010, 05:50 PM

IANA astrophysicist.

But if I remember from undergrad astronomy, a singularity is actually a point of zero volume. So, if any amount of matter is compressed down to a volume of zero it's going to have infinite density.

Admittedly, I can't really wrap my head around the idea of any amount of matter occupying zero space, but there it is.

Chronos

11-15-2010, 05:53 PM

The short answer to your question is that particles are themselves compressible. A longer answer would be that, under the appropriate conditions, the particles change state and become other, smaller particles. A longer answer yet would point out that it isn't physical contact which prevents further compression, like it would be with billiard balls ("physical contact" isn't even well-defined at those scales), but the Pauli exclusion principle, which prohibits two fermions from being in the same state, and you need to look at the whole situation to figure out what constitutes the "same state".

Suburban Plankton

11-15-2010, 06:00 PM

Does the center of a black hole necessarily consist of a singularity? I don't think there's anything that says the density must be infinite, just that it's sufficient to prevent light from escaping. There's a big difference (I think) between "sufficiently dense as to have an escape velocity > c" and "infinitely dense".

Whack-a-Mole

11-15-2010, 06:00 PM

Does Quantum Mechanics allow for an infinitely dense "point" singularity? My understanding is when our current science tries to figure out what a singularity is it pretty much falls apart. Does String Theory offer a different take on a singularity?

Also, I thought a rotating black hole would not form a point singularity but rather a ring singularity and that, in theory, it is possible to avoid the singularity once in the black hole (a non-rotating BH the singularity is unavoidable to anything within the event horizon).

Tom Tildrum

11-15-2010, 06:01 PM

If I remember A Brief History Of Time correctly, Stephen Hawking disliked the concept of singularities so much that he turned time on its side in order to eliminate them from his equations.

RaftPeople

11-15-2010, 06:06 PM

Does the center of a black hole necessarily consist of a singularity? I don't think there's anything that says the density must be infinite, just that it's sufficient to prevent light from escaping. There's a big difference (I think) between "sufficiently dense as to have an escape velocity > c" and "infinitely dense".

IANAP but I read an article that said it depended on how gravity actually works as to whether you get a singularity or not. In some models you get a black hole but you don't get a singularity.

Stranger On A Train

11-15-2010, 06:21 PM

There are two distinct conceptual errors in the o.p. that are leading to the confusion. One is that fundamental particles don't have a set diameter, or even even exist as what we normally think of as particles; instead, they are fields of distributed probability that act about a particular locus. When you push these fields really close together (which requires enormous energy) they sometimes convert to other particles, but they don't just get packed edge to edge like billiard balls in a rack.

The other is that it is wrong to think of a black hole as "infinitely dense", and in fact, really supermassive black holes like that which is hypothesized to be at the galactic nucleus has an average density of less than that of the atmosphere within the event horizon. Instead, what happens is that the slope of the spacetime plenum becomes more and more curved as you approach the hole, until it is such a sharp curvature that you can't climb back out of the hole, and in fact, any energy you put into climbing out actually makes you fall faster. Although this is mathematically represented as a radial curve of increasing curvature which becomes infinite at the singularity point, once you pass the event horizon it is no longer useful to say anything about the spatial properties within. In fact, if you were inside of the event horizon of a black hole that was sufficiently large that the gravitational gradients didn't tear you molecule for molecule you may not even notice that you were inside except that space may appear to be stretched out a little more in front of you than behind you. It is more accurate to conceive of the singularity as being an area where space is stretched out to infinity (albeit within a proscribed boundary) than squeezed into an infinitely tiny space.

And that's just for a non-charged, non-rotating black hole. Once you get into ring singularities and other more exotic discontinuities, you can be excused for dropping a few marbles. Your basic singularity is just a place where someone didn't error check a calculation before compile time.

A longer answer yet would point out that it isn't physical contact which prevents further compression, like it would be with billiard balls ("physical contact" isn't even well-defined at those scales), but the Pauli exclusion principle, which prohibits two fermions from being in the same state, and you need to look at the whole situation to figure out what constitutes the "same state".In fact, a singularity can in many respects be treated as just a really big composite quantum particle, although this makes relativity theorists really unhappy and is generally regarded by the hairdressing community as being a violation of union rules.

Stranger

glowacks

11-15-2010, 06:22 PM

We don't know. In the standard model, the Pauli exclusion principle stops electron/proton plasma from condensing so far, but under high enough pressure they will be forced to form neutrons, which will again be stopped from collapsing up to a point, but in theory they could break into their constituent quarks and gluon at high enough densities. This quark-gluon plasma might be in the center of every black hole, but it might be that the intense gravitational pressure breaks down the laws of physics as we know them and something else happens. Because it's hidden inside a black hole, we can't tell.

We know a lot about neutron stars: we have a theory how they form and their general size, and that they have an escape velocity of a significant fraction of the speed of light. There are lots and lots of examples. We have a few candidates for "quark stars", but nothing as concrete. We've also created quark-gluon plasma in the lab apparently, but it certainly wasn't on the scale that we're looking at for collapsed stars.

I could easily have used some terms wrong here, as I'm just a guy who remembers his one astronomy course in college.

CookingWithGas

11-15-2010, 06:34 PM

There are two distinct conceptual errors in the o.p. that are leading to the confusion. One is that fundamental particles don't have a set diameter, or even even exist as what we normally think of as particles; instead, they are fields of distributed probability that act about a particular locus. Y'know, I actually know better, and sometimes I still get hung up because the word is "particles." :smack:

The other is that it is wrong to think of a black hole as "infinitely dense"...Well, I'm not in a position to argue; I'm just a layman, and read popular press on the subject. But there are many sources that say that it is, or rather, they say that a black hole is that which is bounded by the event horizon and contains a singularity of infinite density at its center. So is this such a common misunderstanding that it's repeated by reputable sources, like NASA (http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html)?

Washoe

11-15-2010, 06:36 PM

If I understand Brian Greene’s books correctly, prior to the inflationary epoch the entire universe is believed to have been packed into an 11-dimensional ball which had a diameter equal to the Plank length. This corresponds to a volume approximately a trillion times smaller than a proton. It also seems that the point particles themselves are simply disturbances in the fabric of space (http://en.wikipedia.org/wiki/Vacuum_energy#Origin). Every time I try to think about it, the only conclusion I can come up with is that there’s nothing really here in the sense that we think of ‘here’ as being ‘here.’ Given that, I have no problem conceptualizing nothing being compressed down to nothing. After that, my brain starts to melt and I just go watch cartoons or something.

Stranger On A Train

11-15-2010, 06:52 PM

But there are many sources that say that it is, or rather, they say that a black hole is that which is bounded by the event horizon and contains a singularity of infinite density at its center. So is this such a common misunderstanding that it's repeated by reputable sources, like NASA (http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html)?Let's say it depends upon perspective. From the outside, it does look "infinitely dense", and that is easier to explain than it having an undifferentiable Riemannian manifold. However, to the particle flying down inside toward a singularity in a really massive black hole, it may just be another day in the office.

Stranger

Chronos

11-15-2010, 07:32 PM

The region within the entire event horizon has a well-defined and finite (and possibly quite small) density. But the core of the black hole has, so far as we can tell, infinite density. To put that a bit more precisely, if you draw some boundary enclosing the center of the hole, then the mass enclosed within that boundary is the same no matter how small you make the volume of the bounded region.

Does the center of a black hole necessarily consist of a singularity? I don't think there's anything that says the density must be infinite, just that it's sufficient to prevent light from escaping. There's a big difference (I think) between "sufficiently dense as to have an escape velocity > c" and "infinitely dense". There is no known physical process sufficient to stop the collapse at any point short of an infinitely-dense singularity. There may well be some unknown physical process which does the trick, and it's widely suspected that quantum gravity might provide such a process, but that of course is only a suspicion.

spenczar

11-15-2010, 08:33 PM

Well, I'm not in a position to argue; I'm just a layman, and read popular press on the subject. But there are many sources that say that it is, or rather, they say that a black hole is that which is bounded by the event horizon and contains a singularity of infinite density at its center. So is this such a common misunderstanding that it's repeated by reputable sources, like NASA (http://imagine.gsfc.nasa.gov/docs/science/know_l2/black_holes.html)?

To elaborate on Stranger's answer, some pictures may help. Recall from General Relativity that gravity warps space. For example, this picture (http://nrumiano.free.fr/Images/bh_warp1_E.gif) shows qualitatively how to think about the warping of space - the "neutron star" here is a more dense star, so it warps space more. Also notice that the size of the depression at the deepest point is just the size of the object which is making the depression itself - this is important.

Black holes are regions where the gravity well is infinitely deep (picture (http://www.h2dj.com/uclaradionews/files/ata/spacetimewarp.gif)). This is what people mean by a singularity.

I'm sure you know that density is just mass / volume. Here's the problem in calculating the density of the black hole: What is the hole's volume?

In one sense, you might say it is infinitely small. The hole goes deeper and deeper, with smaller and smaller radius, down to a single point of infinite depth. At the "bottom" of the depression you should find the size of the object which makes the depression itself, just like with the star and neutron star. But if you do this, you find that the volume of the black hole is infinitely small - zero. Plug this into the density equation, and what do you get? Infinite density.

But in another sense, the density could be relatively thin. A much more common way of measuring the size of the black hole is by demarcating a particular line around the black hole - the "event horizon" - which is the point where the depression is so steep, not even light can escape. This is a pretty sensible definition for the "size" of the black hole, since it everything past the event horizon will permanently be trapped in the hole, but above the horizon there's at least a chance to get out. This horizon also turns out to have a finite radius - and therefore, a finite volume can be described. With a finite volume, you've got a finite density, as well, since the mass of a black hole is finite.

The answer to this, in general, is that people say that the "singularity" is "that thing infinitely far down the gravity well," while the "black hole" is the whole extended object. The singularity therefore does have infinite density, but the black hole (which, headachingly, contains the singularity) does not.

CookingWithGas

11-15-2010, 08:42 PM

Let's move off of infinite density for a moment. Is there some critical mass needed for a black hole to form? That is, why does a neutron star stop smooshing down at some given density, but other matter continues until it forms a black hole--is the only difference the sheer amount of matter, therefore the greater gravity?

spenczar

11-15-2010, 08:45 PM

Let's move off of infinite density for a moment. Is there some critical mass needed for a black hole to form? That is, why does a neutron star stop smooshing down at some given density, but other matter continues until it forms a black hole--is the only difference the sheer amount of matter, therefore the greater gravity?

Yup, and that critical mass is known as the Chandrasekhar limit (http://en.wikipedia.org/wiki/Chandrasekhar_limit).

Chronos

11-15-2010, 09:19 PM

At least, that's for the process by which black holes are formed nowadays. In the very early Universe, when matter was at much greater pressures, it was probably possible to form black holes with smaller masses, which might still be around today (though they would be hard to detect).

And strictly speaking, the Chandrasekhar limit is the limit where a white dwarf collapses into a neutron star, not where a neutron star collapses into a black hole. There's a similar limit for neutron stars, though, which isn't much bigger (probably about 2 solar masses, but the physics of neutron stars isn't as well understood).

spenczar

11-15-2010, 09:25 PM

And strictly speaking, the Chandrasekhar limit is the limit where a white dwarf collapses into a neutron star, not where a neutron star collapses into a black hole. There's a similar limit for neutron stars, though, which isn't much bigger (probably about 2 solar masses, but the physics of neutron stars isn't as well understood).

Totally right, this was a brain-fart of high magnitude. I should've cited the TVO limit (http://en.wikipedia.org/wiki/Tolman%E2%80%93Oppenheimer%E2%80%93Volkoff_limit).

Stranger On A Train

11-16-2010, 07:37 AM

The region within the entire event horizon has a well-defined and finite (and possibly quite small) density. But the core of the black hole has, so far as we can tell, infinite density. To put that a bit more precisely, if you draw some boundary enclosing the center of the hole, then the mass enclosed within that boundary is the same no matter how small you make the volume of the bounded region.Well, I think it is more precise to say that the limit of density as you decrease the size of the boundary goes to infinity. However, while you can define a precise boundary or circumference around a singularity, the radius may be infinite. In any case, matter falling into a black hole isn't smashed together like matter in normal, relatively flat spacetime; it is drawn into a pocket of stretched-out plenum, like a bowling ball suspended on an elastic sheet.

We know a lot about neutron stars: we have a theory how they form and their general size, and that they have an escape velocity of a significant fraction of the speed of light. There are lots and lots of examples. We have a few candidates for "quark stars", but nothing as concrete. We've also created quark-gluon plasma in the lab apparently, but it certainly wasn't on the scale that we're looking at for collapsed stars.Actually, in a sense we know less about neutron stars than we do black holes. A black hole can at least be treated as a fairly simple topological artifact with "no hair" (i.e. there are no processes going on inside that alter the mass, charge, and spin of the black hole), whereas our understanding of neutron stars and the phases they go through are limited by our understanding of what occurs at electron degeneracy pressure. Free quarks aren't stable under normal conditions, and defining the boundary within an object where that stability might occur is not simple, essentially requiring a more complete theory of quantum chromodynamics than currently exists.

Stranger

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