# Do any singularities have Infinite density

1. May 1, 2009

### jamesb-uk

Do any singularities (including the big bang singularity) have:
1. Infinite density
2. Infinite mass
3. Volume
Also, based on the questions above, are naked singularities different to black hole singularities?

2. May 1, 2009

### Nabeshin

Re: Singularities

A singularity with infinite mass makes no sense, so #2 is a no.

#1 and #3 are saying the same thing, because infinite density is a finite amount of mass in a infinitesimal volume. This is the hallmark of gravitational singularities (such as those of a black hole).

3. May 1, 2009

### ZapperZ

Staff Emeritus
Re: Singularities

The van Hove singularity satisfies none of the above description.

Zz.

4. May 2, 2009

### jamesb-uk

Re: Singularities

What is the van hove singularity?

The reason I asked whether singularities have infinite mass was because I heard that black hole singulaities have infinite space-time curvature. This doesn't seem right to me, as if that were true, wouldn't that mean the gravitational attraction of a black hole is infinite.

5. May 2, 2009

### ZapperZ

Staff Emeritus
Re: Singularities

I'm sure you are able to do a search on this yourself.

Note that in your OP, you asked about ANY "singularity". There are a gazillion different types of "singularity", which simply means a quantity, ANY quantity, that diverges at certain values. I happen to have shown you one type of singularity in the electronic density of states.

Zz.

6. May 2, 2009

### junglebeast

Re: Singularities

If there was a singularity with infinite mass then all other particles in the universe would have infinite acceleration towards that singularity, which means that all stars and galaxies would be ripped to shreds in an infinitely small amount of time. The fact that I am alive and typing this message is therefore proof that no object in the universe has infinite mass.

7. May 2, 2009

### jamesb-uk

Re: Singularities

Exactly, that's why I couldn't understand the statement that singulariies have infinite space-time curvature.

8. May 2, 2009

### Nabeshin

Re: Singularities

I find the 2-D rubber sheet analogy to be a good method of resolving this.

http://cse.ssl.berkeley.edu/bmendez/ay10/2002/notes/pics/bt2lfS316_a.jpg

This site has three very good images showing various space-time curvatures of objects with the same mass* but different densities. As you can see in the black hole case, the potential well never ends, and so the curvature is said to be infinite at that point. However, it's just a local effect and far away you can see space-time is curved exactly the same as if the object was the sun.

*As per stellar evolution the masses of these three objects wouldn't be exactly the same, but they're close enough to illustrate the point.

9. May 2, 2009

### diazona

Re: Singularities

Infinite curvature results from infinite density, not infinite mass. And as previously explained, you can get infinite density when you pack any (nonzero) amount of mass into an infinitesimal (you can think of it as basically zero) volume. That's what happens in a black hole, according to general relativity.

And of course, this has also been mentioned before, but a "singularity" is really a mathematical concept that has kind of been extended to physics; it basically just describes a point where something is infinite. Black holes are not the only kind of singularity, although they're probably the most commonly discussed among physicists.

10. May 2, 2009

### diazona

Re: Singularities

This might be interesting: the actual equation from general relativity is

$$R^{\mu\nu} - \frac{1}{2}g^{\mu\nu}R = 8\pi T^{\mu\nu}$$

(well that's one way of writing it, if you ignore the cosmological constant). This represents 16 equations, one for each pair of values of $$\mu, \nu = 0, 1, 2, 3$$ (although some of the 16 are the same). The important point is that all that junk on the left side is, roughly speaking, a measure of the curvature of spacetime (i.e. gravity), and $$T^{\mu\nu}$$ is proportional to the density of matter - not the total mass. The actual mass doesn't appear anywhere in this equation, except as part of the density. So as long as you have infinite density, there will be a singularity (because a term in the equation is infinite), regardless of the total mass involved.

11. May 4, 2009

### Andy Resnick

Re: Singularities

Caustics have infinite energy density. Conversely, wave dislocations have zero energy density.