Thread: singularity

What is a singularity? From what I understand it is a point ... but is there a more precise definition? Arent there things like ring singularities and the like? What make a singularity a singularity?

Originally Posted by tom

What is a singularity? From what I understand it is a point ... but is there a more precise definition? Arent there things like ring singularities and the like? What make a singularity a singularity?

A singularity is just as the name implies: It's a singlearity.
A Ring Singularity is what happens when two singlearity's merge. The union requires a ring. Two of them, to be precise.

The first gravitational ring bearer was a boy named Albert. Albert came up with these rings, so they are called "Einstein Rings."
This is usually done when the rings ask something really stupid and the answer is followed up with, "It's 'such and such,' Einstein!"

Thankfully, Einstein was a Jew.

So when the ring singularity's need an appraisal of their rings, he simply whips out his lens and does some Einstein Lensing.

Some singlearity's refer to ring singularities as a Black Hole.
This is because she's a life sucking bitch from which there is no escape.

A singularity is a mathematical construct, there is no physical definition for one.

As a mathematical construct, a singularity is the name given to a point in which the metric expands into infinities.
A metric tensor or Reimannian metric is used in differential geometry to describe a structure on a differentiable manifold.

Expanding into infinities is a short way of saying that the topological geometry being used and the coordinate system is inadequate for use on a localized space. While a classical coordinate system at a great distance from a black hole is more than sufficient, very near one, it's nowhere near sufficient. It's Too Cotton Picking Big- meaning it lacks Quantum Accuracy.
This is exactly where, in a hundred or more years, QM will come heavily into play in observing the Macro-World.
Without a quantum theory of gravity, we are trapped with classical mathematics that have great difficulty in describing quantum systems.

For a black hole singularity; spacetime cannot be described "smoothly" with classical math.
To "smooth" out the mathematics, you need a class of functions that corresponds with the properties of their derivatives.
Which is not happening when calculating your metric of the "regular" (Regular refers to "smooth" space. Smooth space is described as defined above...) space very near the event horizon of a non-rotating black hole. This is strongly suggestive that we're using the improper coordinate system at this point- NOT that there is a physical object that has zero radius.
These points are called singularities when the motion of matter, when reaching the singularity cannot be determined in a finite amount of time.
However, according to Relativity, an observer who has fallen into a black hole will observe himself fall in a finite amount of time.

A singularity describes a single point whereas a ring singularity describes a Circular Line. Still, these are one dimensional descriptions.

Someday, long after we've established a quantum theory of gravity, we'll need to re-examine Reimannian, Swcharzchild and Lorentz math. As well as the Big Bang theory- it will need updating for greater accuracy.
Someday, long after all of us are dead...

Originally Posted by David M W

A singularity is a mathematical construct, there is no physical definition for one.

Don't take this the wrong way, David, but Neverfly's description (she's a life sucking bitch from which there is no escape) is a pretty good 'physical definition' for me...

Originally Posted by tom

What is a singularity? From what I understand it is a point ... but is there a more precise definition? Arent there things like ring singularities and the like? What make a singularity a singularity?

There is a mathematical definition of a singularity. The singularities in black holes happen when we extrapolate the equations that describe time, space, motion, density and the like to the extreme conditions that exist in a massive collapsing star. However, as it's hard to conduct experiments on what happens in such conditions, we don't really know how well the physics that works outside the black hole, also work inside it.

At least within the context of complex analysis, a singularity is a point where a function is not differentiable. For example, the following functions all have singularities at :







The last one, as a real-valued function, is perfectly well-defined at , but not as a complex-valued function. (If you approach along the real axis, the function approaches zero, but if you approach along the imaginary axis, it approaches .) The second one is not even uniquely defined (every number except zero has infinitely many complex logarithms, which differ by a fixed imaginary increment), but is defined by convention. So you can extend the logarithm to the complex plane in different ways, but you must have a singularity somewhere.

Originally Posted by Coelacanth

At least within the context of complex analysis, a singularity is a point where a function is not differentiable. For example, the following functions all have singularities at :

Something like that may give Tom more of an idea about what he is asking, maybe. The function not only doesn't have a derivative, it doesn't really have a finite value either. Similary he asks about ring singularities (which I could google but I won't), but will be undefined for the circle

Originally Posted by David E. Eaton Sr.

Don't take this the wrong way, David, but Neverfly's description (she's a life sucking bitch from which there is no escape) is a pretty good 'physical definition' for me...

Yes, certainly imaginative!

That said I was talking about how one would physically describe a singularity? And Neverfly sums this up in the first part of his post.

Originally Posted by grapes

Something like that may give Tom more of an idea about what he is asking, maybe. The function not only doesn't have a derivative, it doesn't really have a finite value either. Similary he asks about ring singularities (which I could google but I won't), but will be undefined for the circle

You have me trying to work out what four-dimensional shape that "circle" will form if x and y are allowed to be complex

Just remember that (10, 3i sqrt(11) ) is on it!

And (100, 3i sqrt(11) sqrt(101) )