# Size of a Singularity

#### 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

Staff Emeritus
Gold Member
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

Staff Emeritus
Gold Member
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

Gold Member
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" [Broken], 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.

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#### 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

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#### 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:

esp. Bcrowell's last post with references.

#### Tanelorn

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. Best, 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.

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#### 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

Staff Emeritus
Gold Member
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

Staff Emeritus
Gold Member
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 [Broken] 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.

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