Size of a Singularity: Exploring Mass & Diameter

[daveian]

We are told that at the centre of a black hole lies a singularity; very small and very heavy.
We here a lot about the mass but not the size (diameter) of this object,I asume this is not zero So, incredibly tiny though it may be , it would still bel greater than 0.
Questions;-
What then is the size of a singularity?.
Does it , or could it, vary according to the age and mass of the black hole?
Could the singularity be continually shrinking, ie getting denser with time.It would only get to 0, of course, after an infinitely long time, ie, never.

 

[bcrowell]

The only working theory of gravity that we have is general relativity. According to GR, the size of the singularity is zero. That is basically the definition of the word "singularity." People are working on extending GR to include quantum mechanics, but we don't yet have a theory of quantum gravity. If you ask a physicist to bet a six-pack on it, the most popular guess is that a theory of quantum gravity would give a size for the singularity that was on the order of the Planck length: http://en.wikipedia.org/wiki/Planck_length

 

[WannabeNewton]

The only working theory of gravity that we have is general relativity. According to GR, the size of the singularity is zero.

Isn't the singularity of a rotating black hole a ring of finite size?

 

[SYahoo]

My understanding of the definition of a singularity is: a point of infinite density in space.

With that definition I have always come to the conclusion that it has no size due to the fact a "point" is quantifiable only with only 1 dimension. It may have width, for example, but no height, no depth. After that the math seems easy, 1 x 0 x 0 = 0.

 

[bcrowell]

WannabeNewton made a good point that I was oversimplifying, and SYahoo beat me to answering :-)

I think the most general definition of a singularity in GR is that a spacetime has a singularity if it's geodesically incomplete. What that means is basically that you can have free-falling observers for whom the time measured by a ticking clock cannot be extended arbitrarily far into the past (big bang singularity) or future (black hole singularity). Singularities are not points or sets of points in spacetime, so it's not actually obvious to me how you go about defining the dimension of a singularity in general. (And I think for this reason it also doesn't make sense to define a singularity as SYahoo proposes, as a point of infinite density in space -- it's not a point in space.)

 

[Chalnoth]

In any event, singularities are nonsense. They are areas where the theory breaks down and cannot be taken seriously. I strongly suspect that as you get closer and closer to what General Relativity describes as a singularity, the correct description of what is going on in reality will start to differ dramatically from the General Relativity description. I doubt you have to go all the way to the Planck length for the discrepancies to start.

 

[stevebd1]

Isn't the singularity of a rotating black hole a ring of finite size?

When using elliptical coordinates, the coordinate radius of the ring singularity is equal to the spin parameter a, see the last two images on http://jila.colorado.edu/~ajsh/insidebh/waterfall.html" , the proper radius would be zero at the ring edge.

From what I can gather, only the space-like qualities of the Schwarzschild solution dictate a true singularity, in the case of Kerr metric (and Kerr-Newman & Reissner–Nordström metrics) the supposed singularity resides in time-like space so therefore matter might reside at a stable r, I have seen one or two suggestions that the ring may be super dense matter similar to neutron or quark matter, there also might be a weak singularity at the inner horizon (Cauchy horizon) which supposedly marks the boundary of predictability.

 

[Avijeet]

Are there any observable signatures of singularities? Something that can testify their existence in nature rather than mathematical artifacts.

 

[Chalnoth]

Are there any observable signatures of singularities? Something that can testify their existence in nature rather than mathematical artifacts.

No. All known singularities in General Relativity are hidden behind horizons.

 

[luigidopobici]

is not a black hole a singularity?

 

[Avijeet]

is not a black hole a singularity?

Are you asking that: Is it true that a black hole always contains a point of singularity inside its horizon?

I think the answer is yes. Hope somebody will explain it further.

 

[Chalnoth]

is not a black hole a singularity?

No, absolutely not. A black hole, as we understand it, is an event horizon.

In General Relativity, there exists a singularity inside this event horizon. But that's just a nonsensical statement mathematically, so it can't actually be true. Instead, there must exist some other theory of gravity which accurately describes the state of matter deep inside a black hole. It may be very dense, but it won't be singular.

 

[luigidopobici]

No, absolutely not. A black hole, as we understand it, is an event horizon.

In General Relativity, there exists a singularity inside this event horizon. But that's just a nonsensical statement mathematically, so it can't actually be true. Instead, there must exist some other theory of gravity which accurately describes the state of matter deep inside a black hole. It may be very dense, but it won't be singular.

thanks

 

[JonDE]

If you ask a physicist to bet a six-pack on it, the most popular guess is that a theory of quantum gravity would give a size for the singularity that was on the order of the Planck length: http://en.wikipedia.org/wiki/Planck_length

The only time I've heard a physicist go into detail on it (not sure if I should be quoting him or if I'm even allowed to on this site) he basically said that at all times in reality, every time math predicts something at infinity, nature finds a tricky way out of it. The example he gave was that water spinning down a hole at the exact center should be spinning at an infinite rate, instead what you see is no water at the center.

 

[Tanelorn]

Are there any other possible stable states for collapsed stars between a neutron star and a black hole pseudo singularity? I recall reading about quark stars but could there be others? Could some objects that we think are Black Holes be these instead? If so perhaps these could solve the singularity dilemma?

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

 

[PAllen]

Are there any other possible stable states for collapsed stars between a neutron star and a black hole pseudo singularity? I recall reading about quark stars but could there be others? Could some objects that we think are Black Holes be these instead? If so perhaps these could solve the singularity dilemma?

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

The presumed super-massive black holes at galactic centers are not very dense (thus quark star models are irrelevant) but have event horizons. The indirect evidence for event horizons is compelling, and they may soon be observed directly. See:

https://www.physicsforums.com/showthread.php?t=510860

esp. Bcrowell's last post with references.

 

[Tanelorn]

Pallen thanks for the link. I also found this link:

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


I was mainly trying to find out if there were other denser but stable forms of matter that still had some finite size ie. avoided need for infinitessimals, singularities or Planck sized lengths etc.

 

[Haelfix]

No. All known singularities in General Relativity are hidden behind horizons.

Almost all. Black string solutions in 5 dimensions apparently violate cosmic censorship

 

[Tanelorn]

Pallen, arent all Black Holes pseudo singularities? Therefore their density goes up as their mass increases, and all of which are the most dense forms of matter possible?

 

[PAllen]

Pallen, arent all Black Holes pseudo singularities? Therefore their density goes up as their mass increases, and all of which are the most dense forms of matter possible?

Black holes as a plausible observable phenomenon refer to the event horizon. The galactic black holes show that dense matter explanations to avoid dealing with an event horizon do not work. and steadily increasing evidence, suggests event horizons are a real part of our universe.

What happens inside an event horizon is another matter altogether. For one thing, it is unobservable, in principle, under current theory. GR, as a literal, classical theory says there must be some form of singularity inside, but it is most likely a very chaotic one, not one of the neat exact solutions of GR (still within the realm of classical GR - the exact solutions are unstable - any slight deviation magnifies inside the horizon).

[I ignore the possibility if naked singularities; they are not currently predicted by plausible models within our universe, so far as I know].

What really happens inside the horizon? I know of no physicist who thinks classical GR will continue to hold. So far as I know, no candidate models make meaningful predictions. Inside an event horizon, a quark star provides no additional insight without a working theory of this regime.

Whether a quark star is a possible evolutionary state of some stellar process that, in a few circumstances, avoids an event horizon is an interesting problem in stellar dynamics, but irrelevant as a model of black holes.

 

[Octavianus]

What is the difference between a black hole singularity and the Big Bang singularity?
How does one distinguish one singularity from another? Do they have any properties at all?

If we picture the universe as a ball, and a black hole singularity as having infinite gravity can we picture it as a gravity well to the center of the ball; to the Big Bang itself?

If there is no Hawking Radiation (it has never been proved, right?) is it possible that black holes feed the Big Bang itself? Since time does not exist under infinite gravity there is no before and after between the two singularities, and since a singularity does not exist within the geometry of the universe, aren't all singularities thus the same singularity existing in the "same place"?

 

[Tanelorn]

I just wanted to explain my question again:

Most Physicsts agree that there is likely no true singularity and that what is required is a theory of quantum gravity to explain what is going on. Some say that the singularity inside a black hole is of the order of the Planck length ie. one notch above a true singularity. I am asking if there are intermediate states of collapse to prevent matter collapsing to this state?

If heavy enough a massive star can collapse to a neutron star.
A heavier star might collapse to some other denser stable form of matter eg. a quark star.
A still heavier star might collapse to some other denser form of matter which is still larger than the Planck length.
A still heavier star might collapse to a black hole whose singularity is the Planck length above.
A super massive black hole has collapsed to a Planck length singularity, but the mass and thus density is higher than the previous case.

This is the question I am asking.

 

[Chalnoth]

Are there any other possible stable states for collapsed stars between a neutron star and a black hole pseudo singularity? I recall reading about quark stars but could there be others? Could some objects that we think are Black Holes be these instead? If so perhaps these could solve the singularity dilemma?

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

So far these objects are entirely hypothetical without any evidence in support of their existence.

 

[bcrowell]

No, absolutely not. A black hole, as we understand it, is an event horizon.

In General Relativity, there exists a singularity inside this event horizon. But that's just a nonsensical statement mathematically, so it can't actually be true. Instead, there must exist some other theory of gravity which accurately describes the state of matter deep inside a black hole. It may be very dense, but it won't be singular.

There is nothing mathematically nonsensical about a singularity. For instance, one of the things that makes Hawking and Ellis such a slog to get through is that there are many, many pages of mathematical preliminaries in which they carefully define everything mathematically so that there is no lack of rigor when proving things like the Hawking singularity theorem.

If you want to say that the mathematical singularity in a black hole is not to be taken seriously as representing something physical, then I have the impression that the majority of physicists would probably take your side of the bet if a six-pack was at stake.

Since black-hole singularities in GR are hidden behind event horizons, we will of course never get a chance to check by any direct observation whether they are really singular or not. The singularity that we do get to observe is the big bang singularity.

I doubt you have to go all the way to the Planck length for the discrepancies to start.

Is this based on something you have seen published, or is it just a gut feeling? If the former, it would be interesting to see a reference. It would also be interesting to know whether you think the same thing applies to the big bang singularity.

 

[bcrowell]

Hi, Octavianus,

Welcome to PF!

What is the difference between a black hole singularity and the Big Bang singularity?
How does one distinguish one singularity from another? Do they have any properties at all?

We have a FAQ entry that explains the difference between black hole singularities and the big bang singularity: https://www.physicsforums.com/showthread.php?t=506992 There are also differences among black hole singularities. Their observable properties are mass, angular momentum, and charge.

If there is no Hawking Radiation (it has never been proved, right?) is it possible that black holes feed the Big Bang itself? Since time does not exist under infinite gravity there is no before and after between the two singularities, and since a singularity does not exist within the geometry of the universe, aren't all singularities thus the same singularity existing in the "same place"?

I'm not completely following you here, and you might also want to check PF's rules https://www.physicsforums.com/showthread.php?t=414380 on overly speculative posts. I think there is a pretty well defined sense in which black-hole singularities are separate from the big bang singularity, which is that there are geodesics that are incomplete (meaning that the proper time on the geodesic can't be extended arbitrarily far), and are incomplete both in the past (at the big bang singularity) and in the future (at the black hole singularity). Since these geodesics have nonzero proper times from beginning to end, the two singularities are separate.

 

[PAllen]

I just wanted to explain my question again:

Most Physicsts agree that there is likely no true singularity and that what is required is a theory of quantum gravity to explain what is going on. Some say that the singularity inside a black hole is of the order of the Planck length ie. one notch above a true singularity. I am asking if there are intermediate states of collapse to prevent matter collapsing to this state?

If heavy enough a massive star can collapse to a neutron star.
A heavier star might collapse to some other denser stable form of matter eg. a quark star.
A still heavier star might collapse to some other denser form of matter which is still larger than the Planck length.
A still heavier star might collapse to a black hole whose singularity is the Planck length above.
A super massive black hole has collapsed to a Planck length singularity, but the mass and thus density is higher than the previous case.

This is the question I am asking.

And I've been trying to explain that the question as posed is not meaningful.

Neutron stars are presumed to exist, and are not black holes. Quark stars, if they existed, would not be black holes. Both of these are alternatives to the formation of event horizons - the collapse stops before the event horizon forms.

Meanwhile, an event horizon can form with a sufficiently large assembly of matter with quite low density (e.g. for a black hole with the mass of our galaxy, the density when the event horizon was crossed would only be that of water).

Further, once an event horizon is formed, GR predicts that no matter what form matter takes, nothing can stop the formation of a zero volume singularity inside. Quark stars or neutron stars would be of no 'help' at all inside the event horizon. The only thing that would relevant here is new physics.

 

[Chalnoth]

There is nothing mathematically nonsensical about a singularity. For instance, one of the things that makes Hawking and Ellis such a slog to get through is that there are many, many pages of mathematical preliminaries in which they carefully define everything mathematically so that there is no lack of rigor when proving things like the Hawking singularity theorem.

If you want to say that the mathematical singularity in a black hole is not to be taken seriously as representing something physical, then I have the impression that the majority of physicists would probably take your side of the bet if a six-pack was at stake.

Since black-hole singularities in GR are hidden behind event horizons, we will of course never get a chance to check by any direct observation whether they are really singular or not.

The problem is that if you don't hide the singularities in some form in the math, you can use the singularities to prove anything at all. They destroy the whole theory if they are taken seriously. This is a general problem in mathematics, and is why not dividing by zero is such a strict rule.

The singularity that we do get to observe is the big bang singularity.

Not at all. Except, perhaps, to say that there wasn't one. If we admit the big bang singularity as real, then we have no explanation for why different parts of the universe had the same temperature at the emission of the CMB.

Is this based on something you have seen published, or is it just a gut feeling? If the former, it would be interesting to see a reference. It would also be interesting to know whether you think the same thing applies to the big bang singularity.

This is just based upon how the limits of other physical laws work. They tend to be relevant in interesting ways quite far from their characteristic limits. For example, special relativity's limit is the speed of light, and yet with very accurate experiments we are able to see its effects with observations of objects moving many orders of magnitude more slowly.

Now, because the Planck length is so incredibly short, we don't necessarily expect to see any evidence of quantum gravity any time soon. We might have to get within a few orders of magnitude of the Planck length to see such evidence, and right now we're around 16 orders of magnitude away.

 

[bcrowell]

The problem is that if you don't hide the singularities in some form in the math, you can use the singularities to prove anything at all. They destroy the whole theory if they are taken seriously. This is a general problem in mathematics, and is why not dividing by zero is such a strict rule.

No, this is completely incorrect. Micromath has written a nice FAQ about infinity: https://www.physicsforums.com/showthread.php?t=507003 Feel free to take a look at Hawking and Ellis as well. Note that I have supported my statements with references to the scientific literature, and you have not.

Not at all. Except, perhaps, to say that there wasn't one. If we admit the big bang singularity as real, then we have no explanation for why different parts of the universe had the same temperature at the emission of the CMB.

Please provide a reference to a peer-reviewed paper to support this assertion.

 

[Chalnoth]

No, this is completely incorrect. Micromath has written a nice FAQ about infinity: https://www.physicsforums.com/showthread.php?t=507003 Feel free to take a look at Hawking and Ellis as well. Note that I have supported my statements with references to the scientific literature, and you have not.

You may have noticed in reading that that some operations done with infinity leave undefined results. The answer in math is, "don't do that operation!" But when we are dealing with a physical object, we can't a priori define how it is going to interact or not interact, and those undefined results lead to undefined behavior. That's not necessarily a problem for a theory that is only expected to be a description of reality that may not always be correct: then we can just hide the undefined behavior and say that our theory makes no statement about what happens there. But it is a problem if we take the undefined behavior as being real. Once you do that, you can no longer hide the undefined behavior, and all of reality becomes nonsensical.

Please provide a reference to a peer-reviewed paper to support this assertion.

Do I seriously need to? The horizon problem is a well-known problem with the big bang theory, and is unavoidable if you take the big bang singularity seriously.

 

[Tanelorn]

PAllen, I am not interested in the event horizon. My question is can the collapse to a true singularity be stopped at the quark level or some other form of matter level in the same way that a lower mass stops at the neutron star level. I am just trying to find a way out of an infinite density true singularity.

You are saying that all event horizons always have to mean there is a mathematical singularity inside. Do you have the proof for this? I presume that this means the maths has failed and we have yet to find out what real world Physics is preventing the true singularity?

 

[PAllen]

PAllen, I am not interested in the event horizon. My question is can the collapse to a true singularity be stopped at the quark level or some other form of matter level in the same way that a lower mass stops at the neutron star level. I am just trying to find a way out of an infinite density true singularity.

Not a chance with current physical theories. With some successor theory to SM+GR, I presume yes, but there is no way (I know of) to guess what the nature of this maximally collapsed state is. A string theorist might say it is a cat's toy (ball of string ).

Meanwhile, the quark star has actually been proposed as model of something that forms instead of an event horizon.

 

[PAllen]

You are saying that all event horizons always have to mean there is a mathematical singularity inside. Do you have the proof for this? I presume that this means the maths has failed and we have yet to find out what real world Physics is preventing the true singularity?

These are called the singularity theorems. Yes, it is presumed that they imply that GR breaks down somewhere inside the event horizon. I have said this 3 times already - new physics is the only answer. But nobody knows what applies instead. Picking a random object that is part of known theories *outside* event horizon and guessing - does this stop the collapse inside? - is meaningless. I might as well say that if pink frosted donuts form, the collapse stops.

 

[Chalnoth]

PAllen, I am not interested in the event horizon.

One of the interesting things is that it may be possible to describe everything about a black hole by only describing the event horizon.

My question is can the collapse to a true singularity be stopped at the quark level or some other form of matter level in the same way that a lower mass stops at the neutron star level. I am just trying to find a way out of an infinite density true singularity.

You need a new theory of gravity for this. General Relativity won't allow it.

You are saying that all event horizons always have to mean there is a mathematical singularity inside. Do you have the proof for this? I presume that this means the maths has failed and we have yet to find out what real world Physics is preventing the true singularity?

Yes, it is a proven theorem in General Relativity that if you have an event horizon, there is a singularity inside it. See here:
http://en.wikipedia.org/wiki/Penrose–Hawking_singularity_theorems

 

[Chronos]

It seems safe to say we do not grasp the physics at work inside the BH event horizon. Infinite density creates paradoxes that probably cannot be resolved without a working [and testable] theory of quantum gravity.

 

[Chalnoth]

Infinite density creates paradoxes that probably cannot be resolved without a working [and testable] theory of quantum gravity.

Those paradoxes can only be resolved by making the density not actually infinite.