# Question: what exactly is a singularity?

1. Jan 11, 2010

### C.Braestrup

hi!, just wondered what exactly is a singularity?
yes i could google it, but i figured you guys were smarter.
on forehand, thanks.

2. Jan 11, 2010

### Wallace

In general, a singularity is the concept of a mathematical function returning an infinity or some other misbehaviour. The mathematical definition is explained well at http://mathworld.wolfram.com/Singularity.html" [Broken].

For example, the function f(x) = 1/x 'is singular', i.e. has a singularity, at x=0.

Now, I assume however (correct me if I'm wrong) that you are asking your question in relation to Black Holes? In this case, the solution to the equations of General Relativity that describe Black Holes 'goes singular' at r=0 (where r is the radius from the centre of the Black Hole). What this almost certainly means is that the physical theory (in this case GR) is incomplete, and the fact that the solution contains a singuarity is strong evidence for that. That means you should not think of 'the singularity' of a black hole as being some object with some property. The fact is our equations don't work there, so we just don't know what goes on.

Fortunately, when it comes to black holes what is really important is the event horizon that surrounds the hole. Our equations do behave sensibly here, and we have observed things consistent with the existance of event horizons. Since anything that travels past this horizon cannot be observed again, it doesn't matter what goes on in the middle, as far as we know. Of course we'd still love to know the details, and this is in part the kind of problems that so called 'unified' theories of physics are hoping to one day solve.

Note that there is also a singularity in the solutions to GR for an expanding universe. This one occurs when the scale factor, a(t) (roughly speaking the relative size of the Universe as a function of time), goes to a=0 at some t. In the same way, this should not be thought of as having physical significance, even though it is very common to wrongly assert that this represents the moment of the 'Big Bang'. In fact it once again tells us our equations break down before we get to a=0, so that what we only know what happened back until a time when a(t) has a very small, but non-zero value. Extrapolating further to the a=0 point has no physical justification.

Once again, this is a shortcoming that is being actively worked on by many people, with various different extensions to current theories being examined.

Last edited by a moderator: May 4, 2017
3. Jan 11, 2010

### C.Braestrup

thankyou, alot! you saved my day!

4. Jan 11, 2010

### Matterwave

Also of note are the so called "naked singularities". These are theoretical objects that are singularities, but due to certain properties they possess (e.g. angular momentum) do not have an event horizon. At no point near the singularity is there an area beyond which light cannot escape. If such objects exists, they would be of great use to our understanding of singularities since they would be the only singularities we could observe. These naked singularities are very odd, and as such, the likelihood of them existing is small.

5. Jan 12, 2010

### C.Braestrup

again, thanks