Size of Black Holes: A Closer Look

[jaydnul]

So are all black holes infinitely small, which is what they call the singularity point? I'm talking about the actual distance the matter of a black hole takes up. Does a super massive black hole have the same physical size as any other black hole(which i guess would be infinitely small) and just a must larger radius of effective gravity?

 

[cosmik debris]

The event horizon, the only part of the black hole that you can "see", is proportional to the mass that generated the black hole. The best theory of gravity we have, General Relativity, predicts that there is a singularity at the centre. General Relativity is thought to break down in this regime and quantum effects take over.

 

[Naty1]

The singularity at the very center of a BH is a point of virtually zero size...a singularity.
About all we know is that it appears space and time get mixed up there in quantum fluctuations...a quantum foam. No matter is believed to exist inside a BH...it has been compressed out of existence.

'Big' and 'small' BH refer to the size of the external event horizon...It's usually quoted with a radius r dependent of the mass M which has been swallowed: r = 2M called the Schwarzschild radius. This turns out to be a solution of formulas from Einstein's general relativity...Once something goes inside the event horizon, nothing gets out.

Check out the first section here for more:

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

 

[jaydnul]

So the event horizon is proportional to the mass that generated the black hole(so maybe a collapsing star...). but is all of that mass that used to be the star condensed into an infinitely small point, or is it just packed more tightly together than it was in the star, making it have a measurable radius of actual matter that makes it up.(say a couple kilometers or something...)

 

[phinds]

So the event horizon is proportional to the mass that generated the black hole(so maybe a collapsing star...). but is all of that mass that used to be the star condensed into an infinitely small point, or is it just packed more tightly together than it was in the star, making it have a measurable radius of actual matter that makes it up.(say a couple kilometers or something...)

It's really called a "singularity", not in the sense of a point, but in the sense of "we really don't know WHAT is going on in there".

As was pointed out, the math says it is a dimensionless point with infinite density, but that just means it's where the math model that we currently use breaks down and again, "we really don't know WHAT is going on in there".

The hope is that some day a theory of quantum gravity will explain what's REALLY happening.

 

[jaydnul]

I still haven't really got my answer. (Im probably not being clear enough). Are ALL black holes an infitely small point and their area of gravitational influence is what makes them big or small? Or are there black holes the size of, say, a marble, or the earth, but much much denser? (But there's actual matter making it up and to get to the singularity of the BH you would have to "dig" through physical matter).

 

[phinds]

I still haven't really got my answer. (Im probably not being clear enough). Are ALL black holes an infitely small point and their area of gravitational influence is what makes them big or small? Or are there black holes the size of, say, a marble, or the earth, but much much denser? (But there's actual matter making it up and to get to the singularity of the BH you would have to "dig" through physical matter).

According to the math, the only difference in "size" of a black hole is due to the amount of matter that goes in. The singularity is exactly what I described in my previous post, regardless of the amount of matter.

EDIT: and the "size" is the diameter of the event horizon.

 

[Buckleymanor]

It's really called a "singularity", not in the sense of a point, but in the sense of "we really don't know WHAT is going on in there".

As was pointed out, the math says it is a dimensionless point with infinite density, but that just means it's where the math model that we currently use breaks down and again, "we really don't know WHAT is going on in there".

If we don't know what is going on in there in the inside, how can we say with any conviction what's going on, on the outside.That could apply to the size of the event horizon regardless of how much mass has been used to make it.
We therefore won't know what the speed of mass at the singularity might be moving at, and therefore the size of it's event horizon might not give an indication of the amount of mass used to make it.

 

[AnTiFreeze3]

If we don't know what is going on in there on the inside how can we say with any conviction what's going on in the outside.That could apply to the size of the event horizon regardless of how much mass has been used to make it.
We therefore won't know what the speed of mass at the singularity might be moving at, and therefore the size of it's event horizon might not give an indication of the amount of mass used to make it.

It's been stated several times that General Relativity works for the outside of the event horizon, but not the inside. There's no current theory that explains what goes on in the inside.

 

[Buckleymanor]

It's been stated several times that General Relativity works for the outside of the event horizon, but not the inside. There's no current theory that explains what goes on in the inside.

That does not explaine what happens on the outside of the event horizon for the reasons given.
That's a fudge.

 

[AJ Bentley]

I still haven't really got my answer. (Im probably not being clear enough). Are ALL black holes an infitely small point and their area of gravitational influence is what makes them big or small? Or are there black holes the size of, say, a marble, or the earth, but much much denser? (But there's actual matter making it up and to get to the singularity of the BH you would have to "dig" through physical matter).

You are having a problem with 'infinite'. Some infinitely small black holes are infinitely smaller than others. ;)

Black holes aren't just some sort of black 'star' hanging in the sky that swallow anyone who gets too close. They are places where time and space literally end. We can't even guess what that might mean for the existence of matter.

Long before you get to the singularity itself, ordinary matter ceases to exist as first the orbiting electrons are forced into the nucleus then the nucleus itself is crushed into ? and then snuffed out as space itself ceases to exist and time ends.

 

[stevebd1]

So are all black holes infinitely small, which is what they call the singularity point? I'm talking about the actual distance the matter of a black hole takes up. Does a super massive black hole have the same physical size as any other black hole(which i guess would be infinitely small) and just a must larger radius of effective gravity?

If you want you could impose Planck units which are suppose to be the boundary that length, mass and time lose meaning (some theories predict that the mass within black holes collapse to within about 50% of Planck density) though due to rotation, I think the whole idea of an absolute singularity is mute (in some ways, an absolutely static black hole is on par with the likes of reaching absolute zero K or reaching the speed of light, i.e. it's not possible) every BH, no matter how slight, will have some degree of rotation, which means there may be an inner horizon where time-like worldlines are reinstated, the singularity may reside at the surface of this horizon or within where due to the time-like worldlines, mass wouldn't have to collapse to r=0.

 

[WannabeNewton]

Just to clarify...not all black holes have a point - singularity. Rotating (kerr) black holes have ring singularities.

 

[Naty1]

It's been stated several times that General Relativity works for the outside of the event horizon, but not the inside. There's no current theory that explains what goes on in the inside.

This is incorrect.

That is NOT what has been stated.

GR works inside the event horizon down to the singularity...at the singularity GR and QM break down...it is only at the singularity that we have no theory...this is pretty clearly described in the above posts...

 

[leroyjenkens]

How can something have infinite density? That would mean the volume is zero, right? If the volume of something is zero, then how can it even exist? Zero volume would be literally nothing.

 

[phinds]

How can something have infinite density? That would mean the volume is zero, right? If the volume of something is zero, then how can it even exist? Zero volume would be literally nothing.

So do you think maybe that's why we say that the singularity is the place where the math / models just break down and don't give meaningful answer?

 

[Buckleymanor]

So do you think maybe that's why we say that the singularity is the place where the math / models just break down and don't give meaningfull answer?

It's a leap of imagination to allow something that does not have a meanigfull answer to have one.
If the math on on the inside is not right how can the math be right on the outside unless one allows for wishfull thinking.

 

[Buckleymanor]

GR works inside the event horizon down to the singularity...at the singularity GR and QM break down...it is only at the singularity that we have no theory...this is pretty clearly described in the above posts...

Only at the singularity!

How can GR work if it does not explain the singularity.It's nonesense, you would be better off explaining how an egg boils.
Sorry if this sounds abrupt but to state with conviction that we know how GR works inside the event horizon down to the singularity is just plain wrong.

 

[K^2]

If the math on on the inside is not right how can the math be right on the outside unless one allows for wishfull thinking.

Physics isn't meant to be a blueprint to reality. Being part of reality, we have no way of verifying anything to be absolutely correct. Physics is meant to describe what we can observe. General Relativity describes everything we can observe perfectly, as far as we can tell. Certainly, with higher precision than you could hope for with "wishful thinking".

Whether GR describes anything bellow the event horizon properly is an open question. But it's also irrelevant. Absolutely nothing that's happening bellow event horizon could influence anything above. So frankly, as far as Physics goes, it's not relevant. GR works up to event horizon, and that's all it needs to do. Unless we find a flaw in GR's predictions we can test, to the best of our knowledge, it just works. And since absolutely no experiment can be performed on anything bellow event horizon, any failures of GR in that region are of no significance.

 

[Buckleymanor]

Whether GR describes anything bellow the event horizon properly is an open question. But it's also irrelevant. Absolutely nothing that's happening bellow event horizon could influence anything above. So frankly, as far as Physics goes, it's not relevant.

Tosh! how can you arrive at any conclusion is beyond any known Physics.We don't know if it's of any influence or if it's relivant or not.Why bother looking, might as well say we know as much as we ever will about gravity inside an event horizon so it is of no importance.

And since absolutely no experiment can be performed on anything bellow event horizon, any failures of GR in that region are of no significance.

We have not actualy performed any experiments just outside of any event-horizons so it's jumping the gun to say the least that non can be performed on anything bellow.
We just don't know at this moment.

 

[K^2]

We have not actualy performed any experiments just outside of any event-horizons so it's jumping the gun to say the least that non can be performed on anything bellow.
We just don't know at this moment.

We have a model that works for everything from satellites to neutron stars. And while we have not performed any critical experiments, we have looked at stuff falling into the black hole, and that does seem to agree with theory.

Granted, we cannot absolutely exclude possibility that right next to event horizon all physics as we know it breaks down and something different happens. But we cannot absolutely exclude possibility of existence of pixies and unicorns, either. Yet you aren't going to go around claiming that we just don't know. We do know. At this point, possibility of GR being completely wrong is in realm of fantasy and fairy tales.

It could not be entirely precise. There might be corrections that would alter the location of event horizon, for example. Or some additional contributions to gravity to explain motion of distant galaxies. But it's not going to be something that invalidates GR. Merely corrects it. Just like GR did not invalidate Newtonian Gravity in general. We could predict the motion of distant moons before GR, and we could after.

 

[phinds]

We have not actualy performed any experiments just outside of any event-horizons so it's jumping the gun to say the least that non can be performed on anything bellow.
We just don't know at this moment.

Uh ... you don't seem to quite get the concept of event horizon and why we can't perform experiments below it and never will be able to, by definition.

 

[PeterDonis]

event horizon and why we can't perform experiments below it and never will be able to, by definition.

That's not quite correct. Experiments can be performed below the horizon, but information about their results can never be sent back outside the horizon.

 

[phinds]

That's not quite correct. Experiments can be performed below the horizon, but information about their results can never be sent back outside the horizon.

Yeah, you are right of course and I thought about adding exactly that in my post, but it seemed irrelevant to the point of the incorrect statement I was addressing.

 

[Buckleymanor]

We have not actualy performed any experiments just outside of any event-horizons so it's jumping the gun to say the least that non can be performed on anything bellow.
We just don't know at this moment.

Uh ... you don't seem to quite get the concept of event horizon and why we can't perform experiments below it and never will be able to, by definition.

Well if we can't that by definition would be an experiment to verify if it were a black hole.

 

[Warp]

I still haven't really got my answer. (Im probably not being clear enough). Are ALL black holes an infitely small point and their area of gravitational influence is what makes them big or small? Or are there black holes the size of, say, a marble, or the earth, but much much denser? (But there's actual matter making it up and to get to the singularity of the BH you would have to "dig" through physical matter).

According to General Relativity a singularity inside a black hole has zero volume and finite mass (which effectively makes its density infinite.) According to it, it's impossible for it to have non-zero volume because no particle inside the event horizon can avoid moving towards the singularity. (Even going forward in time makes the particle go towards the singularity. No amount of energy can stop it from moving towards it. In fact, and ironically, applying energy would only accelerate it towards the singularity.)

The "size" of a black hole is determined by its mass. The mass doesn't change even if it's compressed into a singularity. (And "size" refers to the radius of the event horizon, which in itself isn't anything physical. It's simply a zone of curved spacetime with some specific characteristics. The most prominent one is that whatever goes in can never come out.)

A singularity doesn't need to be a point. For a non-rotating, non-charged black hole it's a point, but in practice no black hole is like that because stars always rotate. (So-called primordial black holes, if they exist, might in theory be an exception to this.) In a rotating black hole the singularity will actually be a ring of zero volume (a so-called ring singularity.)

If we consider GR on its own, there's no reason to believe that singularities don't exist. That's because everything that we can measure seems to conform to GR quite well, and so far there's little reason to think otherwise even if we extrapolate to the extremes (such as matter collapsing into its own schwarzschild radius.)

Quantum physics might have an effect on this, and might cause true singularities to not exist, but so far no unified theory has been found to describe this.

 

[pervect]

I still haven't really got my answer. (Im probably not being clear enough). Are ALL black holes an infitely small point and their area of gravitational influence is what makes them big or small? Or are there black holes the size of, say, a marble, or the earth, but much much denser? (But there's actual matter making it up and to get to the singularity of the BH you would have to "dig" through physical matter).

Most people think that the laws of quantum mechanics will mean that a black hole has a finite size. However, we don't know what that finite size is - is it the size of a marble? An atom? Smaller? Nobody knows for sure. We would need a quantum theory of gravity to answer that question, and we don't have one. The theory we do have is GR, but GR cannot answer your question.

GR can tell us other things about black holes though - the size of the event horizon. Gr gives us the schwarzschild radius, and 4*pi*r_s^2 (where r_s is the schwarzschild radius0 is the area of the event horizon.

 

[leroyjenkens]

So do you think maybe that's why we say that the singularity is the place where the math / models just break down and don't give meaningful answer?

So zero volume isn't a meaningful answer? So why is it being reported as the truth?

 

[Warp]

So zero volume isn't a meaningful answer? So why is it being reported as the truth?

It's not "reported as the truth". It's the prediction made by General Relativity.

There are good reasons why that prediction isn't simply discarded as silly. General Relativity has passed test after test with a brilliant score. Almost everything that we can measure seems to conform quite well to its predictions. There are very few scientific theories that have been so well tested and corroborated. It's the reason why when it was discovered that galaxies rotate in an unexpected manner GR was not just thrown out, but instead we are puzzling about what exactly is it that makes them rotate like that. Likewise for the accelerating expansion of the universe.

The same equations predict that particles inside the event horizon of a black hole cannot stay out of the central singularity. A physical impossibility.

The dilemma is, however, that GR does not work well when sizes get very small. GR cannot describe things at quantum levels very well (for instance, GR has no explanation whatsoever for the double slit experiment; reality gets extremely weird at those scales and GR just doesn't work there.)

And that's the problem. You can't get smaller than a singularity, so ostensibly quantum effects might kick into the equation in one way or another. It's yet unknown if and how.

 

[leroyjenkens]

It's not "reported as the truth". It's the prediction made by General Relativity.

Then why do I see "infinite density" and "zero volume" every time I look up information about black holes? If it's a meaningless answer, like the other guy said, why include it as part of the description of a black hole?

 

[Warp]

Then why do I see "infinite density" and "zero volume" every time I look up information about black holes?

Because that's what GR predicts.