View Full Version : Spin of a black hole?

WayneFrancis

2009-Jan-03, 04:55 AM

In answering a question to someone I started thinking. I understand there is some effect to a black hole spinning but I am confused about the actual spin of a black hole and what it means. My question might be a bit fragmented so I'll try to ask it in parts.

How can a singularity actually be said to spin? Doesn't spinning indicate an object with size? (I can't get my head a singularity flattened into a disk)

Would a singularity spin at the speed of light? Would any spinning object condensed down spin at the speed of light due to conservation of angular momentum? Or would a black hole's spin be limited by the speed at which it would have been spinning right at the point the gravity overcomes neutron degeneracy pressure?

gzhpcu

2009-Jan-03, 06:01 AM

When you say "spinning" to you mean rotating?

A rotating black hole can be formed, for example, by the gravatational collapse of a massive rotating star.

A singularity is just the result of a mathematical model. It says the laws of physics based on the model break down (break down at the event horizon). So it is not real in a physical sense.

WayneFrancis

2009-Jan-03, 12:20 PM

When you say "spinning" to you mean rotating?

A rotating black hole can be formed, for example, by the gravatational collapse of a massive rotating star.

A singularity is just the result of a mathematical model. It says the laws of physics based on the model break down (break down at the event horizon). So it is not real in a physical sense.

Yes spinning = rotating. I understand concepts on how black holes form and this is one of the problems.

Lets take a neutron star. Because of conservation of angular momentum as a dead star gravitationally collapses it rotation will increase.

Now I would say that a singularity is more then just a result of a mathematical model. I’m not saying the event horizon is a surface. I’m saying that given what we know matter that overcomes neutron degeneracy pressure will collapse to even a smaller sphere. Given that we don’t know if there is a quark pressure, even if there is, the matter that is spinning will spin faster and faster as it collapses down. The only thing I can think of is since the Schwarzschild radius is the last point which information about the star that formed the black hole could provide information to the rest of the universe then it might retain the rotation rate, to the outside universe, that it had at that point regardless of what happens within that radius

grant hutchison

2009-Jan-03, 01:18 PM

The rotation is embedded in the spacetime around the hole: it affects the orbits of passing objects by "frame dragging", separates out the photon sphere into a zone in which light can follow complex orbits, and creates a region above the event horizon called the "ergosphere" from which energy can be extracted by interacting with the black hole.

The singularity supports this angular momentum by expanding into a ring, rather than remaining a point.

Grant Hutchison

gzhpcu

2009-Jan-04, 11:25 AM

General Relativity predicts that all the matter in a black hole collapses to a geometrical point of radius zero and infinite density (singularity). There is however no way to observationally test this. Our physics breaks down here. Perhaps the matter is really infinitely compressed into a singularity, or perhaps there is some as yet unknown force to prevent an infinite collapse. In the latter case the matter is compressed to a very small size, but not to a point.

No one knows what the singularity is like. Whatever it is, it is governed by physical laws that are not yet understood.

tusenfem

2009-Jan-04, 02:55 PM

General Relativity predicts that all the matter in a black hole collapses to a geometrical point of radius zero and infinite density (singularity). There is however no way to observationally test this. Our physics breaks down here. Perhaps the matter is really infinitely compressed into a singularity, or perhaps there is some as yet unknown force to prevent an infinite collapse. In the latter case the matter is compressed to a very small size, but not to a point.

No, general relativity does not predict anything of the kind!!!

It is the equation of state of matter that determined how much a piece of matter can collapse, so we have:

star: thermal pressure upholds the collapse

white dwarf: degenerate electrons uphold the collapse

neutron star: degenerate baryons uphold the collapse

black hole: something will uphold the collapse to a singularity, however, we don't know what exactly the equation of state for that kind of compressed matter is so, we do not know, as yet, what the upholding force is

No one knows what the singularity is like. Whatever it is, it is governed by physical laws that are not yet understood.

The mathematical singularity.

gzhpcu

2009-Jan-05, 06:50 PM

No, general relativity does not predict anything of the kind!!!

Right you are, thanks for the heads up.

The Theory of Relativity forbids the existence of infinite densities. Therefore, the black hole, with its alleged point-mass singularity, and the Big Bang cosmological point-mass singularity are forbidden by the Theory of Relativity.

source: http://aias.us/documents/otherPapers/IJTP1960%5B1%5D.pdf

grant hutchison

2009-Jan-05, 07:22 PM

Right you are, thanks for the heads up.

The Theory of Relativity forbids the existence of infinite densities. Therefore, the black hole, with its alleged point-mass singularity, and the Big Bang cosmological point-mass singularity are forbidden by the Theory of Relativity.source: http://aias.us/documents/otherPapers/IJTP1960%5B1%5D.pdfHmmm. It would be interesting to see if that one every made it past peer review.

Reading on:

Einstein's conception of the conservation and localisation of gravitational energy are [sic] erroneous.

The current international search for Einstein's gravitational waves is destined to detect nothing.

The concepts of black hole binaries, collisions and mergers are invalid.Edit: Hmmm, again. Controversy. (http://www.wbabin.net/comments/apostol.htm) Crothers appears to be a black hole denier (http://www.thunderbolts.info/thunderblogs/guest1.htm), so perhaps not the best source for a mainstream view of the singularity.

Grant Hutchison

Jeff Root

2009-Jan-05, 09:05 PM

General Relativity predicts that all the matter in a black hole collapses

to a geometrical point of radius zero and infinite density (singularity).

There is however no way to observationally test this. Our physics

breaks down here. Perhaps the matter is really infinitely compressed

into a singularity, or perhaps there is some as yet unknown force to

prevent an infinite collapse. In the latter case the matter is compressed

to a very small size, but not to a point.

No, general relativity does not predict anything of the kind!!!

It seems very close, to me.

It is the equation of state of matter that determine[s] how much a

piece of matter can collapse,

You may consider this to be a nitpick, but I'd say an equation of state

describes a physical system, rather than determines anything about it.

But maybe I misunderstand what an equation of state is. Of course,

being a description doesn't prevent it being used to make predictions.

so we have:

star: thermal pressure upholds the collapse

white dwarf: degenerate electrons uphold the collapse

neutron star: degenerate baryons uphold the collapse

black hole: something will uphold the collapse to a singularity,

however, we don't know what exactly the equation of state for

that kind of compressed matter is so, we do not know, as yet,

what the upholding force is

Last thing first... I can see it working as you say: Knowing the

equation of state could very well lead to figuring out what this

hypothetical force is. However, it would be just as likely to work

the other way around: Knowing the force would lead to figuring

out the equation of state.

Now the main thing:

Yes, thermal pressure prevents the further collapse of stars;

degenerate electron pressure prevents the further collapse of

white dwarfs; degenerate baryon pressure prevents the further

collapse of neutron stars-- but there is no hint of a suggestion

that anything can prevent collapse without limit once a mass has

collapsed within its own Schwarzschild radius. I do think we can

say that unavoidable uncertainty in the location of the collapsing

matter means that it can't be meaningfully described as having a

location more precise than the uncertainty allows. That means it

can't be meaningfully described as compressed to a mathematical

point. A mathematical point, however, is the prediction of general

relativity when one ignores the uncertainties involved.

Oh, I'll also add what I've said a couple of times elsewhere, that

I think-- ignoring the uncertainties involved-- because the mass

continues to collapse without limit, the depth of the gravity well it

makes deepens without limit (relative to the outside Universe, which

can't actually see that part of the gravity well anyway...), so the

infalling matter would require infinite time to reach the mathematical

center, relative to to outside Universe. (But not in its own proper

time, which, because of time dilation, is not only finite but brief.)

-- Jeff, in Minneapolis

WayneFrancis

2009-Jan-06, 05:49 AM

Which brings me back to my question.

As a object spins and starts collapsing its spin speeds up.

Angular momentum of a star is conserved. Given that angular momentum is computed by the following formula

mass x speed of spin x radius = Angular momentum

given that the mass doesn't change as the radius is reduced the rate of spin increases

so If I take the earth as a hypothetical case.

mass is ~ 5.9742 × 10^24 kg but since the mass doesn't matter when it comes to

now the earths Schwarzschild radius is ~9mm. for a slightly easier calculation I'll just say 1cm

now that is about 637,800,000 times smaller so the spin would have to be 637,800,000 times faster

number of seconds in a day is 86,400

~0.00013547 or ~7,382 times a second

obviously a singularity (r=0) has no solution much like most equations have no solution at the singularity

is the spin limited to the spin of the object when it hits the Schwarzschild radius?

I know we supposedly can get 3 pieces of information from a black hole.

Its Mass, its charge and its angular momentum. But since a black hole is considered a singularity what do we use for r? is it the schwarzchild radius? The theoretical radius would be 0 unless there is some quark pressure that holds it up within the event horizon.

The more I think about it the more it makes sense that how fast a black hole spins isn't really the speed that the matter is rotating at but more the speed it was rotating at at the last point where the rest of the universe could get that information from it.

gzhpcu

2009-Jan-06, 07:34 AM

I found this, which I think answers your question:

http://www.if.ufrgs.br/~rns/pr/answers.htm (http://www.if.ufrgs.br/%7Erns/pr/answers.htm)

Why is there a maximal limit for the rotation rates (the spin) of black holes?

This is a prediction from Einstein's general theory of relativity. If a black hole could be made to rotate faster than the maximal spin it would be destroyed! As Kip Thorne puts it: "if the hole were to spin extremely rapidly, centrifugal forces would tear its horizon apart much like they flixig water out of a bucket when the bucket spins extremely rapidly."

The rotation speed of the black hole at its equator is then given by

http://www.if.ufrgs.br/%7Erns/pr/rotation_speed02.gif

where c is the speed of light (approximately 300000 km/s). We can conclude that the maximal spin corresponds to the case where the black hole is rotating at the speed of light, as one would expect.

PS: and it seems that they really do rotate at near to max spin:

http://www.science.psu.edu/alert/Nemmen1-2008.htm

"We think these monster black holes are spinning close to the limit set by Einstein's theory of relativity, which means that they can drag material around them at close to the speed of light," said Rodrigo Nemmen da Silva, a visiting graduate student at Penn State and the lead author of a paper on the new results, which will be presented on January 10, 2008 at the meeting of the American Astronomical Society in Austin, Texas. "Conditions around a stationary black hole are extreme, but around a rapidly spinning one would be even worse," Nemmen said.

gzhpcu

2009-Jan-06, 11:19 AM

No, general relativity does not predict anything of the kind!!!

Not so sure anymore.

Theorems developed by Stephen Hawking and Roger Penrose that quantify the specific conditions under which singularities are the inevitable result of solutions to General Relativity. These theorems demonstrate that in the framework of GR, every black hole must contain a singularity at its center, and all expanding universes like ours must have begun with a big bang singularity.

source: http://www.iscid.org/encyclopedia/Singularity_Theorems

Argos

2009-Jan-06, 12:50 PM

A rotating black hole can be formed, for example, by the gravatational collapse of a massive rotating star.

I think it is generally the case, since we have yet to find a real star that´s not rotating. The Schwarzschild solution is only a generalization. Rotating Black Holes must be the norm.

WayneFrancis

2009-Jan-06, 02:21 PM

I found this, which I think answers your question:

http://www.if.ufrgs.br/~rns/pr/answers.htm (http://www.if.ufrgs.br/%7Erns/pr/answers.htm)

PS: and it seems that they really do rotate at near to max spin:

http://www.science.psu.edu/alert/Nemmen1-2008.htm

thanks for that....I'll read those.

mugaliens

2009-Jan-06, 10:34 PM

A singularity is just the result of a mathematical model. It says the laws of physics based on the model break down (break down at the event horizon). So it is not real in a physical sense.

To piggyback on gzhpcu's comment, many people confuse the term "singularity" with "point." They're not the same. The singularity occurs at the point where the equations are no longer smooth. One singularity occurs at the event horizon, but there are others associated with black holes. There is a point at which matter/energy cannot be compressed any further, and that's the density of a black hole. About 1 Earth mass per teaspoon (roughly). Pretty dense! But not infinate.

grant hutchison

2009-Jan-06, 11:01 PM

There is a point at which matter/energy cannot be compressed any further, and that's the density of a black hole. About 1 Earth mass per teaspoon (roughly). Pretty dense! But not infinate.Hmmm. I'm guessing that's the equilibrium density you predict for matter in the vicinity of the mathematical singularity. That's five or ten times the density of an atomic nucleus, but many orders of magnitude less than the Planck density.

Where did the figure come from?

Grant Hutchison

Jeff Root

2009-Jan-07, 12:10 AM

many people confuse the term "singularity" with "point." They're not

the same. The singularity occurs at the point where the equations

are no longer smooth.

Do the equations become lumpy like soup, or bumpy like an avocado,

or rough like sandpaper, or high friction like unfinished wood, or what?

One singularity occurs at the event horizon,

Yes, but that usually is not the singularity that is meant when talking

about black holes nowadays.

but there are others associated with black holes. There is a point

at which matter/energy cannot be compressed any further, and

that's the density of a black hole. About 1 Earth mass per teaspoon

(roughly). Pretty dense! But not infinate.

You have a point....

.... maybe even two.

First, you are right that matter cannot be compressed by outside

pressure beyond the point at which it collapses into a black hole.

Beyond that point, the matter falls toward the center faster than

pressure can be applied to it, so its density increases without limit

due to its own self-gravitation.

Second, you are right that matter inside the event horizon does

not increase in density in the radial direction, because it is being

pulled apart-- spaghettified-- by the tidal force of its own gravity

in the radial direction. But the radial direction inside the event

horizon is increasingly forward in time, rather than a direction in

space, as you get closer and closer to the center. Very close to

the center, matter is falling practically straight forward through

time, which sort of makes sense since there is hardly any space

left for it to fall through, yet it is still accelerating downward and

still getting spaghettified, with no end in sight. Yet it does reach

the end in very short order in its own proper time. It has an infinite

distance to fall through spacetime (nearly all of it time, rather than

space), and its "perception" of time is dilated, or stretched out, or

slowed (relative to the outside, which can't see it anyhow) by an

amount which increases without limit, asymptotically approching

infinite.

But.... as I've already said a couple of times in the last day or so,

I expect that unavoidable uncertainty in the location of the matter

prevents saying that it has a smaller volume than that uncertainty

allows. So, once the matter collapses within that volume, it really

isn't possible to say what is happening to it. General relativity, by

itself, would say that the matter is still collapsing toward infinite

density at a mathematical point, but the uncertainty principle says

that even if it is doing that, there is no difference from if it isn't.

So it just doesn't matter anymore.

-- Jeff, in Minneapolis

WayneFrancis

2009-Jan-07, 02:34 AM

Well my question is answered and I'm absorbing the reasoning but some comments are muddying the waters here.

As a thought experiment I'd like to talk about a person falling straight into a black hole.

We are all familiar with what the external observer would see and what the falling observer would see.

External observer would see the falling individual seemingly slow down as it approaches the EH eventually fading out while being red shifted

The internal observer would look out and see the universe evolve faster and faster.

To an external observer the faller would be traveling at C when they passed through the EH. But as the math breaks down here the external observer could never see this happen because it would take infinitely long for this to happen. So to the faller if they did, in their own reference frame, pass through the HR they would have to be going at C to all external observers in every frame of reference except their own.

It makes more sense to me that the falling observer would never reach the EH either but see a longer and longer trip ahead of them. This is because of the severe warping of space time. The volume of space when approaching a black hole actually gets larger and larger as you get closer and closer.

The happens at the small scale to. When we measure the volume of empty space at, lets say 1AU then place an object like the sun in the center of that space the volume of that area actually increases slightly. The formula of a sphere

V = 4/3 pi r^3 still works but if you measure the circumference of that same sphere then it does not = 2 pi r. The circumference becomes to small for the radius. The more mass inside that sphere the larger the radius becomes when compared to the circumference. As I understand it the density of the matter also effects the the radius. The more dense the matter the deeper the gravity well is so, ultimately, the longer the radius is. A BH EH is essentially where this gravity well is infinitely deep. So instead of taking a finite amount of time to cross through the sphere you can't even get to the centre anymore.

So to be consistent both the faller and the external observer would never see the faller pass through the point where the EH is.

This all is taking out the idea that a BH may have its EH essentially bubble out because it gains enough mass at its EH that the gravity essentially adds to the mass inside the BH.

All this confuses me even more when I'm told gravity can only travel at C but that is a whole other topic.

gzhpcu

2009-Jan-07, 03:25 AM

The observer would see the faller approach the EH, and ultimately *freeze* at the EH.

The faller, however, approaches the EH faster and faster, and will cross the EH, without noticing it,

NASA has come up with a BH show.

http://www.nasa.gov/vision/universe/starsgalaxies/bh_roadshow.html

A

spaceship could cross the event horizon without noticing it. But that's when things get funky. According to Einstein's theory of general relativity, space itself pours to the center of the black hole like a waterfall, faster than light. As the black hole spins, gas that has entered gets pinned to the sides by centrifugal force, not unlike a thrill-seeker riding a Tilt-a-Whirl.

This wall of gas forms an inner horizon. Gas falls toward the black hole center, but largely this is lifted back out to the inner horizon. The inner horizon is hot and chaotic, with infalling gas and other gas crawling back out. This is about as far as a voyager can get before being vaporized.

Hamilton's Black Hole Flight Simulator:

http://www.youtube.com/watch?v=GYKyt3C0oT4

mugaliens

2009-Jan-08, 12:56 AM

Hmmm. I'm guessing that's the equilibrium density you predict for matter in the vicinity of the mathematical singularity. That's five or ten times the density of an atomic nucleus, but many orders of magnitude less than the Planck density.

Where did the figure come from?

Grant Hutchison

Obviously, the matter density behind the singularity is much greater, to Planck density. My figure was from an old reference wherein the matter was assumed (wrongly) to be evenly distributed within the event horizon.

It serves a good purpose by way of analogy, though.

grant hutchison

2009-Jan-08, 08:44 AM

Obviously, the matter density behind the singularity is much greater, to Planck density. My figure was from an old reference wherein the matter was assumed (wrongly) to be evenly distributed within the event horizon.Ah, thanks. Big galactic centre black holes have "densities" (in that sense) as low as the density of water. The density varies with inverse radius squared. I'm guessing your figure is specifically for a black hole with the mass of the Earth.

Grant Hutchison

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