1. Newbie
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Black Hole Singularity size?

Hello everyone. I've never posted before, so I am not sure if I am doing this right, or if this has been addressed elsewhere already. But here is goes (PS: I love the podcast of Astronomy Cast! Great work.)

There are different size black holes, and the bigger the black hole, the higher gravitational force it has, and the bigger event horizon it has, right? then, does it follow that a bigger black hole has a bigger singularity? or is the singularity the same size, regardless of the size of the black hole?

does singularity have size? (i don't mean the event horizon, but what is at the center of the black hole, the singularity itself)

if singularity does have size, what determines the size of it?

if singularity does not have size, then does it mean that matter that felt into it has disappeared from this universe? (matter has to have size) if matter does disappear, what about conservation of matter? has the matter gone somewhere else? has it converted into energy? into gravity?

Thank you for reading my question.

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Hi, Rob!

No, a singularity has no size. Just like the corner of a sheet of paper
has no size, the center of a circle has no size, or the South Pole has
no size.

But that doesn't mean the matter is no longer there. It is just in a
form that we know nothing about. It is beyond all theories that we
currently have which describe matter, energy, and spacetime.

On the other hand, my understanding of the situation (others will
disagree with this) is that the matter in a black hole is not infinitely
dense. It is not squished down to a true mathematical point.
Instead, the gravity well that is the black hole becomes deeper as
the matter falls farther in and becomes denser. The denser the
matter, the deeper the well. As long as the well keeps getting
deeper, the matter keeps falling toward the center. As long as
the matter keeps falling toward the center, it keeps getting
denser, which makes the well deeper. So the matter never gets
to be a mathematical point, but it approaches a point very
rapidly, and keeps on approaching pointness forever.

It's still weird, but maybe less hard to believe than that the
matter is squished to a mathematical point?

-- Jeff, in Minneapolis

3. Well, as Jeff suspected, I will disagree with that. My (layman's) understanding of a singularity is that it is a point of infinite density, and this is why we cannot describe what form the matter takes. It truly has no size, and all of the singularity's mass is contained at that one point.

The event horizon that surrounds a singularity, however, will have a size that depends on the mass of the black hole.

4. I think we are mixing speculation and known fact here. The singularity is just a point in the mathematical equation where the density function goes to infinity. When this happens the equation is no longer useful to describe what is happening with matter. A new equation is required but that equation is not known yet. That is what the search for a theory of quantum gravity is all about.

Speculation about the form of matter inside a black hole is just that, speculation. It is precisely because we do not know what state the matter is in that we cannot say the density is infinite and that it exists at a point. It doesn't need to be infinitely dense to form a black hole, just sufficiently dense to have an escape velocity greater than c.

5. Hum,
When people talk about the size of a black hole, they usually mean to the size of the event horizon.
The more massive the BH, the larger the event horizon. Or an abstract mathematical idea of zero area, size etc.
The singularity however, is perhaps better imagined to be a minimum size of a plank length. (though a single electron would be 10^-80 cm).

(And to confuse matters, could also be speculated the `singularity ` is not a tiny/mathematical point size, but is a size equivalent to the size of the event horizon. )

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

6. I agree with Blob. The singularity idea is a mathematical result of what we know about physics, carried into a domain far beyond what we can currently observe, and so our theory is not supported by observation there.

It IS possible that inside a black hole there is a single geometric point containing all the mass of a black hole, but it is also possible that this is not the case. We have no easy way to tell the difference right now.

7. Order of Kilopi
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The singularity is a mathematical entity. It is, as Dr Nigel said, a
point of infinite density at the center of a black hole. But since
current physics is unable to describe what actually happens near
the center of a black hole, where the density is ludicrously high,
we don't know whether that mathematical entity has any physical
reality. I suggest that it doesn't... quite.

Do you agree that as the original star collapses to form a black
hole, the density of the matter rises rapidly with no known limit?

Do you agree that as the density increases, the "gravity well"
becomes "deeper"? (That is, the local gravitational field strength
increases and the gravitational potential difference between a
particle inside the black hole and any arbitrary location farther
from the center of the black hole increases.)

Do you agree that the gravitational field strength and the
gravitational potential difference increase at a finite rate, but
without limit?

If so, then I think you must agree that the infalling matter
is always and forever becoming denser as the gravity well is
forever becoming deeper, but infinite density and infinite
"depth" are never reached.

Of course, something (like uncertainty) may prevent the
infalling matter from continuing to increase in density beyond
some limit, in which case the gravitational well would stop
becoming deeper. But either way, whether the matter falls
forever or stops, it does not end up in a singularity. The
singularity is only the mathematical limit of where the matter

-- Jeff, in Minneapolis

8. Singularities

Originally Posted by Jeff Root
The singularity is a mathematical entity. It is, as Dr Nigel said, a point of infinite density at the center of a black hole.
Better, I think, to say that the singularity is interpreted as a point of infinite density, since density itself is a physical quantity. In strict mathematical terms, the singularity is a point where the theory of general relativity is undefined. And that should be interpreted, in my opinion, not as a point of infinite density, but rather as a point where general relativity is invalid. That's the primary motivation for finding an alternative, quantum theory of gravity.

9. Originally Posted by loglo
I think we are mixing speculation and known fact here. ...
But, extrapolation from the known to the unknown is neither speculation nor fact, and it is a valid scientific tool provided it is done with care. The concept of the singularity arises from the equations of GR. Since there is no known mechanism to halt the continued compaction of the matter, we would need some additional reason to think that the singularity is anything other than what the equations tell us.

10. Originally Posted by Dr Nigel
Since there is no known mechanism to halt the continued compaction of the matter...
Title: Quantum mechanics and the generalised uncertainty principle
Authors: Bang, Jang Young; Berger, Micheal S.

The generalised uncertainty principle has been described as a general consequence of incorporating a minimal length from a theory of quantum gravity. We consider a simple quantum mechanical model where the operator corresponding to position has discrete eigenvalues and show how the generalised uncertainty principle results for minimum uncertainty wave packets.

Source

Title: Quantum gravity and minimum length
Authors: Luis J. Garay
(Version v2)

The existence of a fundamental scale, a lower bound to any output of a position measurement, seems to be a model-independent feature of quantum gravity. In fact, different approaches to this theory lead to this result. The key ingredients for the appearance of this minimum length are quantum mechanics, special relativity and general relativity. As a consequence, classical notions such as causality or distance between events cannot be expected to be applicable at this scale. They must be replaced by some other, yet unknown, structure.

11. There is more to learn about this than we can prove as fact. Reading Jeff's post gives a good assertion of what is actually happening on the inside of that event horizon. Mathematically you can pinpoint that what might be the singularity. Reality may be different. Some times that slight ambiguity of the unknown is what makes it interesting. Good on you Jeff.

12. Hum,
Jeff mathematical point works with idealised GR.
(That may be the case but it i think it is unrealistic).
Using quantum theories, below a certain size, space and time become smeared, therefore there cannot be a point source. `Singularities` could stretch to as large as the event horizon.

13. One interpretation I get a kick out of is based on what intense gravity does to time. At the event horizon, time would stop, so anything falling in would freeze there and never get beyond the event horizon. Thus the distribution of mass is not concentrated on an infinitely dense point, but is a hollow sphere instead.

14. Order of Kilopi
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Time does not stop at the event horizon.

Consider this: The location of the event horizon depends on the
location of the observer. The Schwarzschild radius is the location
of the event horizon for an observer at infinity. An observer at a
distance of ten times the Schwarzschild radius would see the event
horizon only a very tiny bit smaller, but an observer at a distance
of one Schwarzschild radius would see the horizon as much smaller.
The horizon is always between the observer and the singularity.
As an observer falls into the black hole, the horizon surrounds him,
but the observer never reaches it. There is always a small opening
directly above him connecting him with the rest of the Universe.
If I fall into a black hole and you watch me from a distance, you
will see me redshift and fade from view as I cross your horizon.
But as the last photon leaves my body that will ever reach you, I
am still moving away from you at high speed, and accelerating,
and I see the horizon far below me. I still see my watch ticking
at what appears to me to be the normal rate. In a sufficiently
large black hole, I could continue to fall for some minutes before
I and my watch are spaghettified. But I will never see myself as
reaching the event horizon. If you see me disappear when my
watch reads 5:00 AM, I may still be in one piece when my watch

The mass in a black hole must in fact be concentrated toward the
center, but an outside observer will not have any clue as to the
distrbution. He can only measure its angular momentum.

-- Jeff, in Minneapolis

15. Blob, good point, I had forgotten how the uncertainty principle would apply. The singularity is predicted by "classical" GR to be a point, but Heisenberg forbids anything from having zero size.

I would therefore guess that the singularity would be not much larger than the Planck length (about 10-35 m IIRC). But it is only a guess. I'm not going to volunteer to go and measure one.

16. Originally Posted by rob00
if singularity does not have size, then does it mean that matter that fell into it has disappeared from this universe?
The collapse of white dwarfs is halted because the amount of infalling mass is not enough to overcome electron degeneracy pressure, which we know about. The collapse of neutron stars is halted because the amount of infalling mass is not enough to overcome neutron degeneracy pressure, which we also know about.

We just don't know what can halt the collapse when the infalling mass IS enough to overcome neutron degeneracy. The infinities that spring from GR mean that the model has broken down completely. But obviously the matter has not disappeared from this universe since its gravitational effect is still present in this universe.

17. Originally Posted by Jeff Root
Time does not stop at the event horizon.

Consider this: The location of the event horizon depends on the
location of the observer. The Schwarzschild radius is the location
of the event horizon for an observer at infinity. An observer at a
distance of ten times the Schwarzschild radius would see the event
horizon only a very tiny bit smaller, but an observer at a distance
of one Schwarzschild radius would see the horizon as much smaller.
The horizon is always between the observer and the singularity.
As an observer falls into the black hole, the horizon surrounds him,
but the observer never reaches it. There is always a small opening
directly above him connecting him with the rest of the Universe.
If I fall into a black hole and you watch me from a distance, you
will see me redshift and fade from view as I cross your horizon.
But as the last photon leaves my body that will ever reach you, I
am still moving away from you at high speed, and accelerating,
and I see the horizon far below me. I still see my watch ticking
at what appears to me to be the normal rate. In a sufficiently
large black hole, I could continue to fall for some minutes before
I and my watch are spaghettified. But I will never see myself as
reaching the event horizon. If you see me disappear when my
watch reads 5:00 AM, I may still be in one piece when my watch

The mass in a black hole must in fact be concentrated toward the
center, but an outside observer will not have any clue as to the
distrbution. He can only measure its angular momentum.

-- Jeff, in Minneapolis
Yes, you will get spaghettified by the extreme tidal forces if you are nearing the SSH. But all this will happen very fast (and violently!) for you!
It is your twin who by length of distance or by means of rocket propulsion manages to stay away who will never actually see you fall past the horizon. For him it would appear as if your time was frozen.

18. The mass in a black hole must in fact be concentrated toward the
center, but an outside observer will not have any clue as to the
distrbution. He can only measure its angular momentum.
Jeff, when you are talking about a Schwarzschild horizon, you are in the context of a static BH and angular momentum is zero. Also is there a solution to the Einstein equations which gives finite (propper) time for the infalling mass. From hence the famous singularity which should NOT exist in a perfectly sane theory even behind a horizon. Historically, the SH seemed first to indicate a truly meaningful baundary at this distance (as the solution found by Schwarzschild broke down at this sphere and went up to infinity). Later a coordinate change allowed to penetrate the horizon and see what should be going on inside.
A static BH is a idealized and unrealistic setting.
A rotating Kerr BH allowes no complete analytical solution and is til to date only poorly understood.

19. Member
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Originally Posted by Dr Nigel
Well, as Jeff suspected, I will disagree with that. My (layman's) understanding of a singularity is that it is a point of infinite density, and this is why we cannot describe what form the matter takes. It truly has no size, and all of the singularity's mass is contained at that one point.

The event horizon that surrounds a singularity, however, will have a size that depends on the mass of the black hole.

but this is what i dont understand. if the singularity is infinite how does a black hole grow? if the singularity inside the black hole is crunched to an infinite density, then why wouldn't the black hole itself remain static no matter how much matter it consumes? or is a significant portion of the matter really compressed between the singularity and the event horizon?

i've always pictured a black hole as sort of like a balloon type structure. like if you filled a water balloon up and turned it upside down. where the black hole that we see is the lip/neck of the balloon while the mass that it consumes is collected "below" what we percieve as space time.

of course this is just my completely meaningless daydream on it lol

20. Order of Kilopi
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Assume the singularity is a point. Assume a million quarks per picosecond are approaching the singularity at about0.99999999999 c from a distance ranging from one picometer to two picometers = massive pile up of quarks, with few if any entering the singularity. Even if we can spagettify quarks to nano plank dimentions, two or more can't enter a point simultaniously, unless quarks can be divided into an infinate number of components? Yes, speculation. Neil

21. The event horizon is defined as the two-dimensional area, in the shape of a sphere, at which light could not escape. In other words, it's just a set of points in space and time defined as meeting a certain mathematical standard, not a physical object. Inside the sphere, the gravitational gradient could be stronger than that amount; outside, it's weaker. If you define the "size" of the black hole as the size of its event horizon, then the way it could "grow" with increasing mass would be that the local space distortion to intensifies so that the defining limit (the set of points past which light can't escape) now describes a bigger sphere than before.

It's like a rope with one end suspended on a pole and the rest of it lying out on the ground extending away from the pole (for some really long distance away, so we're never going to get the whole rope or the other end off of the ground). Some distance away from the pole is the point at which the rope first touches/leaves the ground, depending on which way you look at it: the point from which nearer parts of the rope are in the air and farther parts of it are on the ground. If you increase the pole's height like you're extending a telescope, then there's still a point somewhere along the rope where it meets the ground... but that point is now farther away than it was (and isn't on the same part of the rope as before; it's slid outward along the rope while some parts of the rope that were on the ground are lifted into the air).

And if the pole had other ropes on it in a radial pattern, then those ground-contact points of the various ropes would form a circle... and when the pole extends, those points all move farther out, meaning the circle gets bigger.

22. Order of Kilopi
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Lookout,

The depth of the gravity well (the gravitational field strength)
at the "singularity" (the center of the black hole) is directly
proportional to the time elapsed since the black hole's formation.
Once the black hole forms, the gravity well keeps getting deeper
at the center (if uncertainty or the like doesn't stop it).

The depth of the gravity well at a distance from the singularity
is directly proportional to the mass of the black hole. It never
changes unless mass is added to the black hole.

Delvo,

Your rope analogy is useful, but the more common rubber sheet
analogy is somewhat better. (Rubber sheet analogies are ironic
in that they are intended to show how gravity works, and do it
using gravity as an essential part of the analogy!)

Imagine placing a large, dense mass on a very stretchy rubber
sheet. The sheet sags to the point where the downward force of
the mass is balanced by the elastic force in the sheet. Now
suppose the mass represents a star with several times the mass
of the Sun, at the end of its life. The star collapses and the
remaining core becomes much smaller and much denser. If it
becomes a black hole, it just keeps on collapsing, getting ever
smaller and denser, without limit. The rubber sheet under the
mass is stretched without limit by the increasingly-dense mass.
But the sheet some distance away from the mass is not affected
at all, since the mass is not changing. A marble rolling around
the mass at a distance will continue to roll unaffected as the
mass collapses. A planet orbiting a collapsing star would not
be affected by the star's collapse as long as mass is not thrown
out by the star or added to the star.

What Cougar said about electron degeneracy pressure stopping
the collapse of a star into a white dwarf, and neutron degeneracy
pressure stopping the collapse of a star into a neutron star is
good. Note that no force can stop collapse once a black hole is
formed because forces are transmitted at the speed of light or
slower. Any force that could prevent further collapse of a star
which had already become a black hole would have to be transmitted
faster than light speed, in addition to being extremely strong.

Uncertainty is a different kind of thing, though. It isn't a
force, and might effectively limit the density of the matter and
depth of the gravity well.

neilzero,
Particles falling into a black hole are always pulled apart in
the radial direction. That's what we mean by spaghettification.
Any two particles become progressivly farther apart in the radial
direction as they approach the singularity.

I imagine that where the matter becomes so dense that there is
only room for a single particle, the matter is essentialy a line
of particles falling "straight down" into the gravity well. At
that point the uncertainty in the position and momentum of any
particle is likely to limit the "narrowness" of the well.

-- Jeff, in Minneapolis

23. Order of Kilopi
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Adding to what I just wrote, I believe that a line of particles
falling "straight down" at the center of the gravity well would
be falling in time but not in space. The radial direction in a
black hole is forward in time. In the rubber sheet analogy,
particles could continue to be packed more densely, making the
gravity well become ever deeper, but they would no longer be
moving through space once they reached the point where the
stream is only a single particle wide. They would be falling
forward in time. Almost the opposite of time stopping!

I see the horizontal distance as space, the vertical distance
as time, and distance across the sheet as the actual spacetime
distance.

-- Jeff, in Minneapolis

24. Originally Posted by Jeff Root
Uncertainty is a different kind of thing, though. It isn't a force, and might effectively limit the density of the matter and depth of the gravity well.
I think this idea has a lot of potential. In fact, IIRC, I believe the electron and neutron degeneracy pressures result from this phenomenon: The smaller a "box" you put these particles in, the more "jumpy" they get. This "jumpiness" creates the pressure that restricts further compression. For electrons and neutrons, apparently this restriction is not absolute, and the most extreme gravity can overcome such restriction.

Originally Posted by Jeff Root
Note that no force can stop collapse once a black hole is formed because forces are transmitted at the speed of light or slower. Any force that could prevent further collapse of a star which had already become a black hole would have to be transmitted faster than light speed, in addition to being extremely strong.
Well, no force that we know of can stop the collapse.

I'll have to think about your "speed of light" argument. I don't know why a "garden variety" force that propagates at the speed of light couldn't halt the collapse, which is not occurring any faster than the speed of light.

25. I love this thread. However, this concept of what the nature of matter/energy beyond a Planck length belongs to is philosophy not science. Better think in terms of other Universes, and how converging mass/energy systems create new Universes.

26. Originally Posted by snowcelt
Better think in terms of other Universes, and how converging mass/energy systems create new Universes.
Isn't that awfully philosophical as well?

27. Oh yes! Anything beyond the Planck Constant is philosophy. If a point source is not but a mathematical toy, what is a reality in this nether region but a place for us in philosophy?

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