What is singularity?

Quoting Stephen Hawkin's definition:

"A point in space-time at which the space-time curvature becomes infinite."

Nonetheless I'd like to read a more extended version of this definition from more knowledgeable people.

 

I am not sure that there is a completely accepted technical definition.

Roughly, a spacetime is singular if there is a timelike curve having bounded acceleration (i.e, a worldline an observer could follow) that ends after a finite amount of proper time. Singular spacetimes have "edges".

By the Penrose-Hawking singularity theorems, any "reasonable" classical spacetime must be singular. Very roughly, in any "reasonable" classical spacetime, gravity is so stong that the fabric of spacetime gets ripped, thus creating an "edge".

 

Is it Singularities are a unlimited dense point without any volume?

 

If we observed the Universe as a whole in 11 dimensions would the strength of Gravity increase. Is it possible that the whole 11th Dimensional Gravity of the Universe is just leaking into all the other dimensions of the Universe within our 4D known Space in singlular points causing matter and or virtual particals to get trapped in its 11th dimensional singularity horizon making matter appear to clump together around it in a horizonal orbit?

Just a question, nothing more.

 

A singularity is a mathematical phenomenon based upon the absentia of a physical theorem for quantum gravitation, and not a real physical actuality.

Reference:
http://en.wikipedia.org/wiki/Gravitational_singularity

 

Besides super duper definitions of singularities like Wikipedias', is there anyone else in this forum with sufficient knowledge on this matter that is confidently capable of stating, in the simplest possible terms, what this phenomenon is all about?

 

There's nothing "super duper" about Wikipedia's definition; in fact, it's a pretty loose definition IMO. If you want a simple definition of a spacetime singularity, try this one on for size:

A spacetime singularity is a point in spacetime at which the (intrinsic) curvature of the spacetime is infinite.

That's the simplest explanation I can think of, but it doesn't really do the concept justice. In particular, one can have a more exact definition of a singularity by saying that the singular points of a spacetime are those which cannot be included in the maximal analytic extension of the spacetime, but I guess that's a bit more than you want.

To use the more usual notion (i.e., from popularizations of science such as Hawking's books), a singularity is a point where the predictable nature of physics breaks down because the curvature predicted by general relativity at that point is infinite.

 

Would it be natural to say that a Singularity is a condensed infinite continuum point where all Dimensions could be experienced through observation all at once because of the infinite curvature?

 

No. That sentence doesn't actually make much sense, quite apart from it being the wrong interpretation.

 

The Edge of Infinity: Beyond the Black Hole, by Paul Davies, has a very-good popular-level treatment of singularities. This book gives a tremendous (and quite accurate) explanation of Penrose's first singularity theorem. I even recommend it as a complement to Wald and Hawking and Ellis for physics types encountering for the first time the technical details of singularity theorems.

 

Thanks George.

 

Hmmm, well people who are perhaps more knowledgable than me can correct me, but a singularity is only a singularity from another frame of reference, am I right? In the frame itself there is no singularity right? Hence no breakdown of laws right?

Would be funny if laws in nature would break down, for why would they be defined as laws? :)

 

Wrong actually, a singularity in one frame of reference would be a singularity in any frame of reference.

My definition of a singularity is "a point in space where any of the properties of matter or space-time become singular - i.e. infinite or zero. Thus in the limit density, pressure and space-time curvature become infinite and volume becomes zero.

You can argue whether they actually exist, whether the limit is actually reached, or whether the concept is merely an artifact of an incomplete knowledge of what happens in the extreme conditions as that limit is approached.

Garth

 

Really? So is that described by some kind of theorem or so?

It appears counterintuitive to me.

What could be an infinity to an outside frame of reference does not have to be one locally right?

Take for instance a measurement of an object from an outside frame of reference that becomes a singularity. Time grinds to a halt and volume becomes zero right? But inside, does time stop as well and does voume become zero as well?

Seems that I am missing something here with regards to your assertion that a singularity is frame of reference independent.

 

Are you confusing the singularity itself with the event horizon around that singularity?

At the event horizon around a Schwarzschild BH the coordinate system becomes singular, but that can be transformed away - just as the Lat. and Long. system of coordinates on the Earth's surface becomes singular at the N. & S. Poles. However you cannot transform away the physical singularity at the centre.

At the genuine singularity at the centre there is no time - it doesn't 'grind to a halt', there is no way of measuring it at all, it has become singular.

Garth

 

Sorry, but I am still not getting it.

Let's assume some very small object getting caught by a black hole. At one point it passes the event horizon and after that it gets drawn closer to the center.
Now I understand that for any outside frame of reference (both inside and outside the event horizon) is appears as if the object is going towards a singularity. But for the object itself? How could it become a singularity?

It seems to me, and I suppose I am wrong about it, that a singularity is a singularity for all outside frames of references but that the space-time of an infinitessimal small size regarded as the singularity for the outside frames of references is not.

 

It gets squashed until in the limit its density and temperature become infinite and its volume zero.

I'm not sure I understand that statement. The singularity, at the centre of the event horizon, is a - well - singularity.

Garth

 

Ok then let me reword it.

In GR the measurement of space and time of a particular region depend on the frame of reference right? So a measurement from any frame of reference, which has to be from inside the black whole since from outside one cannot even make a measurement, of the center of a black hole will result in measuring a singularity. No disagreement here. But the area that is the singularity itself, the infinitesimal small region itself, if we place the frame of reference there, then how do you conclude that even there there is a singularity, that is what I don't understand.

 

No, a singularity is a globally defined quantity so it is a a singularity in all frames of reference.

 

Unless it is a theorem or so, stating that it is defined as such is not an answer at all.

Why?

For instance, an object occupying an infinitessimally small region of space drawn inside a black hole does not encounter anything unusual in its local measurements of space and time, even when it is eventually drawn into the singularity. Am I to believe that for that small region everything simply from one point in time to another becomes undefined? Again I fully understand that that is what happens from an observing frame of reference, outside of that particular region, but within the region itself?

It seems to me that the measurement of time and space inside this region does not change at all, initially passed the event horizon, and later towards the center. That principle seems to me one of the fundamental principles of relativity.

Clearly from within the region measurement outside of it would become very different rapidly and I would wonder if not from this region the ouside would appear a singularity!

One should be able to demonstrate that for an object occupying an infinitessimally small region of space that is sucked into a singularity the space and time coordinates inside become infinite or meaningless. Not from a frame of reference outside the object but inside the mentioned region of space.

 

Of course it does, at the singularity itself, (not at the event horizon where just the Schwarzschild coordinates become singular,) there are no measurements of space and time, they have become singular and undefinable,

Yes.

Garth

 

I've read many books, majority of them defines a singularity as a point of infinite density or a point at which laws of physics break down and that spacetime curves in such that the light rays goes crazy. It's quite amazing to know that such a 'thing' may exist.

 

To talk of a singularity in a physical context is just a mathematicians cop out because the simple singularity only applies if you manage to create a black hole with zero angular momentum. This is so nearly impossible that it is really not worth considering in a physical context. It is far more useful to try to understand the properies of a rotating black hole. This is a much more complex and interesting object and a significant amount of analysis of the collapse towards the final "ring singularity" could be done using conventional relatavistic and quantum modelling without any need of a quantum theory of gravity.

I feel that serious modelling of the details of this process and the environments created as the collapse progresses could lead to signifficant insights that could help when the need comes to consider quantum gravity.

The way thse subjects appear to be dismissed is a bit like saying our universe is uninteresting because it all ends with a heat death and forgetting that all the interesting stuff (like life) is actually happening on the way to this final process.