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ritwik
2012-Jun-23, 12:48 PM
it is believed (http://archive.ncsa.illinois.edu/Cyberia/NumRel/BlackHoleAnat.html) that blackhole has infinite density .

if so ,

a blackhole formed out of a 10 solar mass star will have infinite density

a blackhole formed out of 1000000 solar mass star will have infinite density

but if these two blackholes come across each other ,10 solar mass blackhole will be sucked in by 1000000 solar mass balckhole :D

so infinite density of 10 solar mass balckhole is not really infinite ,it is finite and definite:clap: because if both densities were equal then 10 solar mass blackhole would not yield to 1000000 solar mass blackhole

so is it right to say all blackholes have infinite densities (http://en.wikipedia.org/wiki/Black_hole) :doh:

Post edit by admin: I removed the font-color, since by custom here, colors are used to signal moderator action.

korjik
2012-Jun-23, 04:34 PM
why would having an infinite density keep a black hole from being sucked into a larger one?

tusenfem
2012-Jun-23, 05:56 PM
why would a black hole have infinite density?

Strange
2012-Jun-23, 09:24 PM
so is it right to say all blackholes have infinite densities (http://en.wikipedia.org/wiki/Black_hole) :doh:

From that page:

Since the average density of a black hole inside its Schwarzschild radius is inversely proportional to the square of its mass, supermassive black holes are much less dense than stellar black holes (the average density of a 108 solar mass black hole is comparable to that of water)

So, no, it is not right to say that a black hole has infinite density.

pzkpfw
2012-Jun-23, 11:07 PM
Could the OP mean the theoretical (hypothetical?) singularity at the centre?

korjik
2012-Jun-24, 08:11 AM
still leaves my question

ritwik
2012-Jun-24, 02:09 PM
why would having an infinite density keep a black hole from being sucked into a larger one?

INFINITY is one of a kind ...it must be disassociated from singularity:confused:.if 2 blackholes tagged with " infinite densities" interact with each other,bigger one steal the show;) BUT both had same "Infinite density " status, so why 1 become food to another ? well , what guess is ,the larger blackhole created deeper spatial curvature than the other ,so smaller one lost it's footing and slipped in to another:o

well if both had created equal deep space curvature ..and come across each other, ofcourse they will merge into one so what make the difference ?

if we could distinguish both blackholes , mostly after their interaction smaller blackhole will become a part of the larger one (http://accidentalanglocatholic.files.wordpress.com/2012/03/snake-eating-a-snake.jpg) .so we can imagine larger one had a dominitive influence over another ,so thay are not on same infinite density pedestal

also taking in to consideration only 3 or 4 solar mass is required to get the status of balckholes so the word "infinity" associated with it becomes so banal :rolleyes-default:


@PZKPFW YES !!! IM THE OP AND I MEANT IT !!!! is that a problem ?:p

why would theorists say blackhole has Zero Size and Infinite Density (http://www.physicsforidiots.com/blackholes.html).

you know it takes stuff to form a blackhole and when it becomes a blackhole where does all that stuff go ? could the general notion be a mathematical fallacy ? like 1 divided by 0 equals infinty

why balckhole has 0 radius ? is this a done deal ?? even if there is one atom inside a blackhole it will have a radius!! what does blackhole excrete accoring to hawking how does it get stuff to spew out as radiation at the end of it's life ?if this is true balckholes finally drain out universe of all its stuff !! how can a thing formed out of 3 solar mass and 100000000000000000000 solar mass do the same thing at same rate ??there can't be any disparities between infinities ,,right? is it logical to say this infinity isn't much powerful as this?

Jeff Root
2012-Jun-24, 04:25 PM
General relativity predicts that the density of the matter
at the center of a black hole increases without limit as
the matter collapses into a smaller and smaller volume.
The density becomes infinite after infinite time.

-- Jeff, in Minneapolis

Jeff Root
2012-Jun-24, 04:31 PM
ritwik,

What you read was correct. Your interpretation of it
might not be. Nomatter what the mass of a black hole,
the density of the matter at the center is effectively
infinite.

-- Jeff, in Minneapolis

JCoyote
2012-Jun-24, 04:53 PM
It's more accurate to say it has collapsed beyond out ability to measure or effectively model.

As for the mass of a black hole, it is sort of considered the only useful defining characteristic of any particular one. All they have is "mass".

ritwik
2012-Jun-24, 05:01 PM
ritwik,

What you read was correct. Your interpretation of it
might not be. Nomatter what the mass of a black hole,
the density of the matter at the center is effectively
infinite.

-- Jeff, in Minneapolis

what is effectively infinite means- beyond mathematical interpretation OR infinitely infinite ?

and most importantly according to mainstream it will perish at some point of time via process called hawking radiation one one says blackholes last forever

so how does an entity which once labelled as infinity ooze out of existence ?? infinity is FOREVER , don't you think so?

Jeff Root
2012-Jun-24, 05:47 PM
It's more accurate to say it has collapsed beyond our
ability to measure or effectively model.
Anything inside the event horizon of a black hole is
completely beyond our ability to measure, even in
principle. General relativity models what happens
to the matter just fine. It collapses forever. On the
other hand, quantum mechanics says such a thing
is nonsense. So there is a conflict, with no good
resolution yet.

-- Jeff, in Minneapolis

Strange
2012-Jun-24, 10:26 PM
You seem to be so confused, it is hard to know where to start. Especially as you have already read some fairly clear descriptions. But...


why balckhole has 0 radius ?

... lets start here.

Black holes do not have a radius of zero. They have a radius proportional to their mass, the Schwarzschild radius.


is this a done deal ??

No. The matter inside may be compressed to a very high density. Probably not infinite but we don't know. We need a quantum theory of gravity to understand what happens to the matter inside a black hole. String theory has "fuzzballs", for example: http://en.wikipedia.org/wiki/Fuzzball_%28string_theory%29.


what does blackhole excrete accoring to hawking

Black body radiation: http://en.wikipedia.org/wiki/Black_body


how does it get stuff to spew out as radiation at the end of it's life?

There is a description of the event horizon separating pairs of virtual particles and making them real. (But this is not completely accurate and raises
more questions than it answers, in my opinion).


how can a thing formed out of 3 solar mass and 100000000000000000000 solar mass do the same thing at same rate ??

They don't do the same thing at the same rate. They have different mass, different radius, different gravity and radiate Hawking radiation at different rates. They don't really have much in common!


there can't be any disparities between infinities ,,right?

As an aside, mathematically, there is more than one infinity. In fact, there are an infinite number of them ...

Nick Theodorakis
2012-Jun-25, 12:39 AM
It's more accurate to say it has collapsed beyond out ability to measure or effectively model.

As for the mass of a black hole, it is sort of considered the only useful defining characteristic of any particular one. All they have is "mass".

And spin. And charge, at least in principle.

Nick

Jeff Root
2012-Jun-25, 01:29 AM
What you read was correct. Your interpretation of it
might not be. Nomatter what the mass of a black hole,
the density of the matter at the center is effectively
infinite.
what is effectively infinite means- beyond mathematical
interpretation OR infinitely infinite ?
As I said in my first post, general relativity predicts
that the density of the matter at the center of a black
hole increases without limit as the matter collapses
into a smaller and smaller volume, so it becomes
infinite after infinite time. However, it collapses so
quickly into such an extremely tiny volume that the
density is effectively infinite a few milliseconds after
the collapse of a massive star. The matter never
stops collapsing (again, according to general relativity,
which so far appears to be correct in all the situations
that have yet been observed), so it is always becoming
more and more dense. But the density is *effectively*
infinite after just a few milliseconds. For all "practical"
purposes you can consider the density of the matter
to be infinite at that time. There is no way in which
it is not the same as infinitely dense.



and most importantly according to mainstream it will
perish at some point of time via process called hawking
radiation one one says blackholes last forever
Hawking radiation has no relevance to the question
of the density of matter at the center of a black hole.
Hawking radiation is generated at the event horizon.



so how does an entity which once labelled as infinity
ooze out of existence ?? infinity is FOREVER , don't
you think so?
Infinite time has nothing to do with infinite density.

Just because the matter at the center of a black hole
has infinite density doesn't mean it can't evaporate
via Hawking radiation. As yet neither the density of
the matter nor Hawking radiation are certain, but the
two questions are independent of each other.

-- Jeff, in Minneapolis

Jeff Root
2012-Jun-25, 02:30 AM
why would having an infinite density keep a black hole
from being sucked into a larger one?
INFINITY is one of a kind ...it must be disassociated
from singularity:confused:.if 2 blackholes tagged with
"infinite densities" interact with each other, bigger one
steal the show;) BUT both had same "Infinite density"
status, so why 1 become food to another? well, what
guess is, the larger blackhole created deeper spatial
curvature than the other, so smaller one lost it's
footing and slipped in to another:o
Nomatter what the masses of two black holes, they
simply merge when they come together. They become
one. Saying that the less massive one falls into the
more massive one makes sense in that the less massive
black hole accelerates more readily, so it moves farther
and faster due to the force pulling them together. But
they really just merge.



well if both had created equal deep space curvature
..and come across each other, ofcourse they will merge
into one so what make the difference ?
Mass is the property of matter of resistance to
acceleration when a force is applied. Larger mass,
greater resistance to acceleration due to the mutual
gravity of the two black holes. The density of the
matter at the centers of the black holes is irrelevant.



why would theorists say blackhole has
Zero Size and Infinite Density (http://www.physicsforidiots.com/blackholes.html).
The theory of general relativity mathematically
describes how matter and energy warp spacetime,
and how the shape of spacetime affects the motion
of matter and energy. The math shows that when
enough matter is concentrated in a small enough
volume that the resulting pressure overcomes all
the resisting forces, it will be squashed to zero
volume and infinite density. There is nothing that
can prevent it from happening.

Maybe you find the idea of matter having zero
volume and infinite density nonsensical. The theory
of quantum mechanics, which is also very well tested
under less extreme conditions, suggests that it might
only be *almost* zero volume and *almost* infinite
density. So you can take comfort in that.

Even if the volume is zero and the density is infinite,
I have no problem with it.



you know it takes stuff to form a blackhole and when
it becomes a blackhole where does all that stuff go ?
To the center.



could the general notion be a mathematical fallacy ?
like 1 divided by 0 equals infinty
No, if I'm not confused and thinking of special relativity,
I believe that general relativity has been proven to be
mathematically self-consistent. That is a very rigorous
demonstration that it contains no mathematical error of
any kind. It has been examined in minute detail by
thousands of very intelligent people trying to find any
flaw, over the last century. None has been found.



why balckhole has 0 radius ? is this a done deal ??
I agree with Strange that your definition of a black hole
is flawed. However, I disagree with his definition, too.

A black hole is a region of spacetime which is so
strongly warped by the matter and energy in it that
it has an event horizon. However, the event horizon
is not the black hole. The event horizon is simply the
most characteristic feature of a black hole. It is the
surface from which no light can escape. Outside the
event horizon is a volume from which almost no light
can escape. It is part of the black hole, too, even
though it is outside the event horizon. The outermost
feature which sets black holes apart from other things
is what is called "the last stable orbit". No massive
object can orbit inside the radius of the last stable
orbit, which has a radius of 3 times the radius of the
event horizon. Between the last stable orbit and the
event horizon is the "photon sphere", in which light
theoretically could orbit the black hole. That is also
a unique and characteristic feature of black holes.



even if there is one atom inside a blackhole it will have
a radius!!
Matter can be falling into a black hole from the outside
continually, so it can be at all distances from the center.
But the matter at the center is compacted by its own
gravity far too much for any atoms to exist. It is even
far too compact for any baryons or even quarks to exist.
So the matter at the center can have effectively zero
volume and infinite density.

-- Jeff, in Minneapolis

AGN Fuel
2012-Jun-25, 03:47 AM
so infinite density of 10 solar mass balckhole is not really infinite ,it is finite and definite:clap: because if both densities were equal then 10 solar mass blackhole would not yield to 1000000 solar mass blackhole

so is it right to say all blackholes have infinite densities (http://en.wikipedia.org/wiki/Black_hole) :doh:

Not sure about this statement, where you suggest that because two densities are infinite then they are equal. I don't think that you can equate infinite values in such a way. Take numbers for example: the set of numbers is infinite. However, I can take any number and divide it into half, so for any value I choose I must have twice as many 'halves' as I do 'wholes'. Both sets of numbers are infinite, but they are evidently not equal.

Density is mass into volume. If volume is 0, density is infinite by virtue of simple maths. Whether that occurs at the singularity is not yet clear. However, gravitational attraction between two bodies is a function of their respective masses. To that end, it doesn't matter if they are blackholes or fairy cakes, something of 1,000,000 solar masses is going to dominate orbital proceedings with any object of just 10 solar masses. If they merge, you'll have one black hole of 1,000,010 solar masses and the density of its singularity will still be infinite.

ritwik
2012-Jun-25, 05:38 AM
i understand the theory as it is ,i just have trouble conceptualizing the theory

to put it in to words ..if you could cram up this much mass inside this much volume of space you could create an INFINITY (density) RIGHT HERE !! so the word 'INFINITE' becomes somewhat mundane ,i dont know whether it's right to say "singularity density" instead of "INFINITE density" which would be more comforting:boohoo:

also in the process of implosion of a star in to a blackhole ,the split second right before it attains the state of infinite density ..it is does not have infinite density :think:
so just the mere addition of another speck of dust makes the grandeur difference and gives it the occult status of infinity

that doesn't make sense to me :wall:

WayneFrancis
2012-Jun-25, 06:47 AM
it is believed (http://archive.ncsa.illinois.edu/Cyberia/NumRel/BlackHoleAnat.html) that blackhole has infinite density .

if so ,

a blackhole formed out of a 10 solar mass star will have infinite density

a blackhole formed out of 1000000 solar mass star will have infinite density

but if these two blackholes come across each other ,10 solar mass blackhole will be sucked in by 1000000 solar mass balckhole :D

so infinite density of 10 solar mass balckhole is not really infinite ,it is finite and definite:clap: because if both densities were equal then 10 solar mass blackhole would not yield to 1000000 solar mass blackhole

so is it right to say all blackholes have infinite densities (http://en.wikipedia.org/wiki/Black_hole) :doh:

Post edit by admin: I removed the font-color, since by custom here, colors are used to signal moderator action.

No it isn't right to say that. Don't confuse density with mass. We don't know if everything inside the event horizon collapses to a single point. If it does then that would count as a point of infinite density regardless of the amount of mass involved. The mass/energy is what warps space time.

A 10 solar mass black hole doesn't just move towards a larger black hole with out the larger black hole moving towards the smaller. It is just the amount of movement is correlated with the masses involved.

Basically the definition of a black hole being a point in spaces time with infinite density is unprovable and more a popular science way of conveying what we believe to be happening to a point then continuing on with with that understanding without really knowing what the laws of physics are really like at those extremes.

WayneFrancis
2012-Jun-25, 06:58 AM
what is effectively infinite means- beyond mathematical interpretation OR infinitely infinite ?

and most importantly according to mainstream it will perish at some point of time via process called hawking radiation one one says blackholes last forever

so how does an entity which once labelled as infinity ooze out of existence ?? infinity is FOREVER , don't you think so?

Again you don't have the science right here. What happens inside of the EH is currently unknown. We can model it to a very long way using physics as we know it. As Jeff has said if things are collapsing inside the BH then from a outside observer that collapse would take an infinity long period of time. I don't know any mainstream model that says black holes will last forever because they experience hawking radiation. Once the temperature of the CMBR dips below surface temperature of a black hole from the point of view of a distant observer then that black hole will start to evaporate. The smaller the black hole the higher its temperature. Small black holes are hotter then large black holes. If you want to think of a point of infinite density then think of it this way...at that point in time that state has not yet been achieved. From the outside observer the material would still be falling into the centre.

Strange
2012-Jun-25, 07:19 AM
i understand the theory as it is ,i just have trouble conceptualizing the theory

I'm not sure you do understand...


to put it in to words ..if you could cram up this much mass inside this much volume of space you could create an INFINITY (density) RIGHT HERE !!

We can't see inside a black hole. Our current theories fail to predict what happens in the center of a black hole; i.e. they predict a singularity an infinite value. I think it is generally agreed that this indicates that the theory is incomplete (we don't have a theory of quantum gravity). I doubt there is an infinite density.

But even if there were an infinite density, it doesn't matter. All we can experience is the effects outside the event horizon where the black hole behaves as an extended object with finite (and quite low) density.

I would just forget the whole infinite density thing. It's probably not real and seems to be pretty irrelevant. Unless you are a researcher developing theories of quantum gravity.

WayneFrancis
2012-Jun-25, 07:21 AM
i understand the theory as it is ,i just have trouble conceptualizing the theory

to put it in to words ..if you could cram up this much mass inside this much volume of space you could create an INFINITY (density) RIGHT HERE !! so the word 'INFINITE' becomes somewhat mundane ,i dont know whether it's right to say "singularity density" instead of "INFINITE density" which would be more comforting:boohoo:

also in the process of implosion of a star in to a blackhole ,the split second right before it attains the state of infinite density ..it is does not have infinite density :think:
so just the mere addition of another speck of dust makes the grandeur difference and gives it the occult status of infinity

that doesn't make sense to me :wall:

You don't need infinite density to get a black hole. All you need is enough mass within a given radius. If you had a mass of water that was 7AU in radius that would = a black hole. There would be an event horizon even though the object has a density of 1,000.00 kg/m3

Of course this is ignoring the fact that we don't know any sub atomic forces that can hole up to that amount of gravity. If you could make a 7AU radius ball of water appear it would quickly collapse under its own gravitation weight. To an outside observer though it would be a instant black hole even before collapsing simply because there is enough mass within its own Schwarzschild radius.

Like others like Jeff have said we understand the physics even inside the EH but this is because we assume that the laws don't just suddenly change just because we can't observe them.

So for our ball of water that we magically created it had a density of water that very instant. What happens 1 second after the creation inside the event horizon? That question doesn't make sense from the outside observers frame of reference. If you created a boat on the surface of that ball of water we can tell you what would happen there too. The ball of water would collapse at a finite rate of speed. The boat remember was at 7AU and thus even at light speed would take almost 1 hour to reach the singularity. The boat, and any occupants on it, wouldn't make it that far but they might make it relatively fine for a portion of the trip.

ritwik
2012-Jun-25, 10:17 AM
→blackhole does not have infinite density:D
→if you squish any object (star pen paper pencil) smaller than its schwarzschild radius and it will become a blackhole
→studies are still going on regarding properties of blackholes which calls for a GUT

thanks:whistle:

NEOWatcher
2012-Jun-25, 12:47 PM
→if you squish any object (star pen paper pencil) smaller than its schwarzschild radius and it will become a blackhole
I don't look at the formation of a black hole as a "squishing" of an object.
Certainly under that much gravity, the object will become more dense, but the real thing going on is that the gravity is continually increasing at the object's surface. Eventually that surface gets lost when gravity is enough to be a black hole.
That's where I personally stop because we don't really know what happens to that mass and I don't have a good enough grasp of spacetime to know how measurements really are affected. Just that as our measurements deal with c, our frame of reference will not approach the surface.

ritwik
2012-Jun-25, 04:23 PM
i speculate studying more about what happens inside blackhole give us more insight into the properties of mass ..:liar:

because like jeffroot (http://www.bautforum.com/showthread.php/135738-blackhole-Vs-blackhole?p=2031175#post2031175) said
But the matter at the center is compacted by its own gravity far too much for any atoms to exist. It is even far too compact for any baryons or even quarks to exist.

the total mass of BH's must equal total mass of stuff that went into it's making

but when blackhole evaporate by hawking radiation what comes out as radiation is photons (http://casa.colorado.edu/~ajsh/hawk.html) ,but we know photons does not have mass !! only thing goes out of BH's are photons when it evaporates and photons does not have mass

so blackholes must still have mass within it even if all stuff evaporate as radiation

Hornblower
2012-Jun-25, 04:35 PM
i speculate studying more about what happens inside blackhole give us more insight into the properties of mass ..:liar:

because like jeffroot (http://www.bautforum.com/showthread.php/135738-blackhole-Vs-blackhole?p=2031175#post2031175) said

the total mass of BH's must equal total mass of stuff that went into it's making

but when blackhole evaporate by hawking radiation what comes out as radiation is photons (http://casa.colorado.edu/~ajsh/hawk.html) ,but we know photons does not have mass !! only thing goes out of BH's are photons when it evaporates and photons does not have mass

so blackholes must still have mass within it even if all stuff evaporate as radiationYou can speculate all you want, but that will not keep energy loss from a system from reducing its mass, as I think I understand 20th century physics. If your remark was true, then fusing hydrogen into helium would not result in a loss of mass, when measurements show clearly that the alpha particle has less mass than four separate protons. Most of that lost mass is carried away as gamma radiation.

It appears to me that you have a lot to learn about the fundamentals of modern physics.

ritwik
2012-Jun-25, 05:15 PM
You can speculate all you want, but that will not keep energy loss from a system from reducing its mass, as I think I understand 20th century physics. If your remark was true, then fusing hydrogen into helium would not result in a loss of mass, when measurements show clearly that the alpha particle has less mass than four separate protons. Most of that lost mass is carried away as gamma radiation.

It appears to me that you have a lot to learn about the fundamentals of modern physics.

yeah i know. i'm just a wee bairn at physics actually im interested in cosmology as hobby, but its all about physics.. and i cant just shut up

so your saying gamma radiation has mass ..what i learned is, all radiation is massless and moves at 'c'

jfribrg
2012-Jun-25, 05:53 PM
I think the confusion comes from a misunderstanding. Perhaps the OP is confusing infinite density to mean infinite mass. The mass in a black hole is not infinite. It is a finite amount that gets continually compressed into a smaller and smaller volume (the singularity at the center of the black hole). Two black holes interact with each other in much the same way as any two massive objects do : the gravity of each causes them to accelerate toward each other with the less massive object experiencing the greater acceleration. What happens when the event horizons merge is trickier because of the previously noted absence of a unified field theory.

Tensor
2012-Jun-25, 06:01 PM
yeah i know. i'm just a wee bairn at physics actually im interested in cosmology as hobby, but its all about physics.. and i cant just shut up

so your saying gamma radiation has mass ..what i learned is, all radiation is massless and moves at 'c'

Yeah, that's not quite true. It's a good first approximation for those who are just learning physics, but there is a more accurate model. Photons do not have a rest mass, that's where the expression radiation is massless comes from. If a photon could be brought to rest, it would have a mass of zero. However, photons always travel at c, so they have momentum, which carries energy. Energy and mass are equivalent and can be converted between each other using the conversion factor of c2.

Oh, and it's not mass that causes gravity. In General Relativity, its energy and pressure. A mass causes gravity based on the energy contained in it. Again, using c2 to convert the mass to energy.

Jeff Root
2012-Jun-25, 06:06 PM
Mass is a form of energy. Energy can change from one
form into another. That is what happens when Hawking
radiation is emitted from a black hole. The mass at the
center of the black hole is converted to radiation at the
event horizon via the gravitational force. Even if the
particles created at the event horizon are massless, they
carry away the energy of the mass at the black hole's
center, so the mass decreases.

The particles created at the event horizon are separated
by the gravitational force from the black hole's mass.
The mass lost is the "mass equivalent" of the escaping
radiation. m=E/c2

-- Jeff, in Minneapolis

WayneFrancis
2012-Jun-26, 01:27 AM
i speculate studying more about what happens inside blackhole give us more insight into the properties of mass ..:liar:

because like jeffroot (http://www.bautforum.com/showthread.php/135738-blackhole-Vs-blackhole?p=2031175#post2031175) said

the total mass of BH's must equal total mass of stuff that went into it's making

but when blackhole evaporate by hawking radiation what comes out as radiation is photons (http://casa.colorado.edu/~ajsh/hawk.html) ,but we know photons does not have mass !! only thing goes out of BH's are photons when it evaporates and photons does not have mass

so blackholes must still have mass within it even if all stuff evaporate as radiation

But photons, no matter how long their frequency, have a rest mass equivalent.

E=mc^{2}
Photone has energy of E. If you want to know its rest mass equivalent then solve for m
m=\frac{E}{c^{2}}

Every time a photon of Hawking radiation is emitted the mass of the black hole is decreased by that amount.

caveman1917
2012-Jun-26, 03:20 PM
As I said in my first post, general relativity predicts
that the density of the matter at the center of a black
hole increases without limit as the matter collapses
into a smaller and smaller volume, so it becomes
infinite after infinite time. However, it collapses so
quickly into such an extremely tiny volume that the
density is effectively infinite a few milliseconds after
the collapse of a massive star. The matter never
stops collapsing (again, according to general relativity,
which so far appears to be correct in all the situations
that have yet been observed), so it is always becoming
more and more dense. But the density is *effectively*
infinite after just a few milliseconds. For all "practical"
purposes you can consider the density of the matter
to be infinite at that time. There is no way in which
it is not the same as infinitely dense.

The infalling matter reaches the singularity (or forms the singularity if we're talking about the first collapse) in a finite amount of proper time, so the density at the singularity becomes infinite in a finite time. If on the other hand we're considering an outside observer rather than one attached to the infalling matter we should note that the event horizon is an edge to his spacetime, the "inside" of the black hole doesn't exist in his universe. So neither does the singularity. All he has is an event horizon that appears to behave as if it has a certain mass. Since he has a notion of circumference of this event horizon, he can say that the density of the black hole is that mass divided by the volume that would be in a sphere of that circumference, giving the figure Strange quoted. However in any case that concept of density is somewhat contrived, since the volume of the black hole to an outside observer is ill-defined. In neither case does the density approach infinity in the limit of infinite time.

noncryptic
2012-Jun-26, 04:34 PM
General relativity models what happens
to the matter just fine. It collapses forever.

GR models a lot things just fine -as verified by observation-. However..


Nomatter what the mass of a black hole,
the density of the matter at the center is effectively
infinite.

Only if that unverified prediction by GR is in accordance with reality.
But scientific consensus seems to be that the very fact that GR predicts infinity, means GR breaks down at/near the center of a black hole.
At any rate, a Schwarzschild radius is large enough to hide something larger than zero size.


To the OP:
Infinite density does not mean infinite momentum.

Jeff Root
2012-Jun-26, 04:44 PM
caveman,

I agree that the concept of density of a black hole is
somewhat contrived because the volume is ill-defined.

However, it is my understanding (I read it somewhere...)
that the density of the matter at the center approaches
infinite in infinite time. That makes sense to me because
nothing can stop the matter from collapsing further than
it has already collapsed.

The reason the volume of a black hole is ill-defined is
that it increases with time, as the distance from the
event horizon to the center increases. The volume is
proportional to the black hole's age.

Can you explain what is meant when you say that
infalling matter reaches the singularity in finite proper
time of the infaller? I have accepted that assertion as
true even though it seems to contradict the assertion
that the distance to the center is always increasing,
which I also accept as true.

-- Jeff, in Minneapolis

Strange
2012-Jun-26, 04:46 PM
That makes sense to me because
nothing can stop the matter from collapsing further than
it has already collapsed.

Nothing we currently know of.

antoniseb
2012-Jun-26, 05:02 PM
Just some hand-waving: General Relativity may be to points in space as Thermodynamics is to individual particles... i.e. only relevant when dealing with large collections of them, but wonderfully accurate and predictive once you have enough. For all those thinking that black holes are geometric points, this is the basic idea as to why we say we don't know what happens in such extreme situations.

Jeff Root
2012-Jun-26, 05:07 PM
General relativity models what happens to the matter
just fine. It collapses forever.
GR models a lot things just fine -as verified by observation-.
However..


Nomatter what the mass of a black hole, the density
of the matter at the center is effectively infinite.
Only if that unverified prediction by GR is in accordance
with reality.
But scientific consensus seems to be that the very fact
that GR predicts infinity, means GR breaks down at/near
the center of a black hole.
BAUT is the only place I see people saying that GR
"breaks down" at or near the center. What I get from
other sources is that GR predicts a singularity, while
QM predicts that a singularity is impossible. That is
the conflict. The singularity by itself does not appear
to be a problem, and *near* the predicted singularity
is certainly not a problem by itself. It only becomes
a problem when QM is considered in addition to GR.

I say that the density of the matter at the center is
effectively infinite because even a microscopic physicist
falling into a black hole, making observations as he
approaches the center, would see no significant
difference from infinite density, nomatter how close
he got. Again, that is according to GR, not QM.

-- Jeff, in Minneapolis

Strange
2012-Jun-26, 05:22 PM
BAUT is the only place I see people saying that GR "breaks down" at or near the center.

Really? I have seen the same thing stated in many places; perhaps expressed in slightly different words such as "outside its domain of applicability" "unable to make predictions", etc.

Just the first few I came across:

A singularity is a region of space-time in which gravitational forces are so strong that even general relativity, the well-proven gravitational theory of Einstein, and the best theory we have for describing the structure of the universe, breaks down there.
http://www.pbs.org/wnet/hawking/strange/html/singular.html


Many theories in physics have mathematical singularities of one kind or another. Equations for these physical theories predict that the ball of mass of some quantity becomes infinite or increases without limit. This is generally a sign for a missing piece in the theory
[it then goes on to discuss various types of singularities, including those at the centre of a black hole]
http://en.wikipedia.org/wiki/Gravitational_singularity


In the context of spacetime theory, singularities are limits (or, loosely speaking, "regions") in which the Einstein field equations break down.
http://people.bu.edu/pbokulic/blackholes/


According to general relativity, these are singularities – regions where Einstein's field equation breaks down.
http://web.physics.ucsb.edu/~gary/

noncryptic
2012-Jun-26, 06:32 PM
BAUT is the only place I see people saying that GR
"breaks down" at or near the center.

My reference is Sean Carroll ("From Eternity to Here"/the arrow of time).


What I get from other sources is that GR predicts a singularity, while
QM predicts that a singularity is impossible.
...a problem when QM is considered in addition to GR.

Why 'believe' one over the other? The fact that both say something different and neither says something useful about the core of a black hole (which corresponds to the first few tiny fractions of a second after the big bang), is saying that we don't really know. That's why those domains are not part of the standard model.

It's one thing to say GR predicts a singularity, it's another to say the density at the center "is" (effectively) infinite.
I'd say anything short of infinite is not effectively infinite, in fact it is infinitely far removed from infinity.

But perhaps more importantly: wrt a singularity being real there is no verification by means of observation.

Ie we don't say the speed of light is constant regardless of the motion of the observer just because GR says it is, we say that because we can observe it. That can't be said about a singularity.

Jeff Root
2012-Jun-26, 07:53 PM
What I get from other sources is that GR predicts a
singularity, while QM predicts that a singularity is impossible.
...a problem when QM is considered in addition to GR.
Why 'believe' one over the other? The fact that both say
something different and neither says something useful
about the core of a black hole ...
GR says the energy must form a spacetime singularity
at the center of a black hole. That is useful. QM says
particles can't occupy zero volume. That is useful, too.



It's one thing to say GR predicts a singularity, it's
another to say the density at the center "is" (effectively)
infinite.
I'd say anything short of infinite is not effectively
infinite, in fact it is infinitely far removed from infinity.
Our descriptions of black holes come from GR. GR says
matter in a black hole must collapse forever. So any
observer falling into a black hole and getting as close
as nonhumanly possible to the center would always
see the density as indistinguishable from infinite.

It is analogous to saying that photons are massless.
Attempts to measure photon mass are consistent with
a value of zero. So we say the value *is* zero.



But perhaps more importantly: wrt a singularity being
real there is no verification by means of observation.
Yes. It is "just" a theory. It is an important concept
to distinguish theory from observation, but that applies
to everything. It isn't more important in the question
of whether black holes have singularities than, say,
the question of whether bees can fly.



Ie we don't say the speed of light is constant regardless
of the motion of the observer just because GR says it is,
we say that because we can observe it. That can't be said
about a singularity.
I agree completely ... but ... Just as I choose to say that
photons are massless rather than saying that the photon
mass is less than such-and-such, I choose to say that
the matter in a black hole is compressed to *effectively*
infinite density. It fits what we *do* know.

-- Jeff, in Minneapolis

Shaula
2012-Jun-27, 05:00 AM
It is analogous to saying that photons are massless. Attempts to measure photon mass are consistent with a value of zero. So we say the value *is* zero.
Except there are sound theoretical reasons for the photon's mass to be zero. If it were not then Electroweak would be in trouble. I know of no analogous constraint for black holes that would support an infinite density.

caveman1917
2012-Jun-27, 10:46 PM
However, it is my understanding (I read it somewhere...)
that the density of the matter at the center approaches
infinite in infinite time. That makes sense to me because
nothing can stop the matter from collapsing further than
it has already collapsed.

The matter hitting the singularity is something that makes it stop collapsing further.


The reason the volume of a black hole is ill-defined is
that it increases with time, as the distance from the
event horizon to the center increases. The volume is
proportional to the black hole's age.

Proportional to the black hole's total lifetime, not to its age until the present time. So sticking with GR (no hawking radiation) and thus black holes that last an infinite time, the volume of the black hole is infinite. It always is. However that doesn't mean it's ill-defined, if it were it would be well-defined, just infinite. The problem is that that is only one of a number of equally good arguments that can be made as to what "volume of the black hole" means. Another argument would be that the volume is zero since the inside of the black hole is outside the edge of the outside observer's spacetime, and volume is a function of space (which ends at the event horizon as far as the outside observer is concerned). Yet another argument puts the volume at \frac{4}{3} \pi r^3 where r is defined as the radius of curvature of the event horizon. Ill-defined means that taking different (equally correct) routes to the answer gets you different answers. The most prudent answer is perhaps to say that the notion of "volume" is simply not meaningful in this case and leave it at that.


Can you explain what is meant when you say that
infalling matter reaches the singularity in finite proper
time of the infaller? I have accepted that assertion as
true even though it seems to contradict the assertion
that the distance to the center is always increasing,
which I also accept as true.

I'm not sure what you mean by that the distance to the center is always increasing, but if we assume it is then it doesn't necessarily contradict that the particle doesn't reach the center in finite time. If the speed of something increases faster than that the distance it has left increases then it will reach its destination in finite time. I presume there are coordinates in which your assertion about increasing distance is correct, but then in those coordinates the speed increases faster, because the physical results must be the same in all coordinates and there are coordinates in which it reaches the singularity in finite proper time.

What you perhaps mean is that the proper distance to the singularity for an infaller is infinite? That is correct, but note that the speed of the infaller also goes to infinity near the singularity, such that the total time on his clock for reaching the center is still finite. You can find a full derivation here (http://en.wikipedia.org/wiki/Gullstrand%E2%80%93Painlev%C3%A9_coordinates#Speed s_of_raindrop) (wiki).

publiusr
2012-Jun-30, 08:28 PM
To quote an old OMNI magazine blurb "some infinities are larger than others." An infinite subway tunnel could easily swallow many drinking straws that are infinitely long themselves. Rudy Rucker has a nice book called "Infinity and the Mind" that is a joy to read.

loglo
2012-Jul-01, 06:19 AM
BAUT is the only place I see people saying that GR
"breaks down" at or near the center. What I get from
other sources is that GR predicts a singularity, while
QM predicts that a singularity is impossible. That is
the conflict. The singularity by itself does not appear
to be a problem, and *near* the predicted singularity
is certainly not a problem by itself. It only becomes
a problem when QM is considered in addition to GR.

I say that the density of the matter at the center is
effectively infinite because even a microscopic physicist
falling into a black hole, making observations as he
approaches the center, would see no significant
difference from infinite density, nomatter how close
he got. Again, that is according to GR, not QM.

-- Jeff, in Minneapolis

The issue with singularities in GR is not infinite density, it is geodesic incompleteness. You have chunks missing from what is meant to be a smooth, differentiable manifold. GR is a global theory, not just in space but in time. Geodesics should be extendible over the entire manifold, singularities prevent that. Hawking and Penrose's definition of a singularity is:-


A spacetime is singular if it is timelike or null geodesically incomplete, but can not be embedded in a larger spacetime.
http://arxiv.org/abs/hep-th/9409195

Interestingly enough the first hint of possible non-singular black holes in QG showed up just this past week:-
A no-singularity scenario in loop quantum gravity by Martin Bojowald, George M. Paily (http://arxiv.org/abs/1206.5765)

Note that they also couch their definition of singularity in terms of geodesic incompleteness.

The singularity problem of general relativity states that space-time is generically incomplete, with only finite ranges of time over which we can extrapolate in some directions.

noncryptic
2012-Jul-01, 04:23 PM
> But perhaps more importantly: wrt a singularity being
> real there is no verification by means of observation.



Yes. It is "just" a theory. It is an important concept
to distinguish theory from observation.

The issue is not lack of distinction between theory and observation.

The issue is that in science an idea about how some aspect of the world works is not formally a theory unless it has been verified by observation. To put it differently: in science a theory is never "just" a theory.