# Why do we define such a thing as singularity?

According to general relativity, an observer not in the close proximity of a black hole, observing a mass fall into that black hole, will never see that mass cross event horizon(it will gradually fade but never actually pass through the event horizon) as it requires an infinite amount of time to do so. So, effectively, for the observer, the mass of the object falling in will never reach the middle of the event horizon, or the so called "singularity", as it will require more-than-infinite amount of time to do so.

Then why do we even define such a thing as a singularity?

I am alright with the singularities in space-time curvature, but not with a finite amount of mass being compressed into zero volume, not because it is silly, because it would never happen in a finite time for a casual observer outside of black hole.

-
I am not sure what the actual question is. We don't define any singularity but rather just notice that it is a consequence of the GTR. As for what happens under the horizon: no external observer will ever observe it, so you can ignore singularities if you want (most people would ignore black holes completely anyway, if it wasn't for Star Trek). Nevertheless, it's interesting to ask what your theory tells about the situations you can't yet observe (i.e. you extrapolate the theory). – Marek Nov 17 '10 at 0:47
BTW, the singularity is not in the "middle" of the event horizon. An observer who passes through the horizon does not find the singularity at some particular spatial location, rather it is in their future. That's why they can't avoid it. It's like death and taxes. – pho Dec 16 '10 at 19:20
Yes, yes, I have grown much more knowledgeable about the issue of singularity since I asked the question. Thank you for your concern Jeff. – Cem Dec 16 '10 at 19:44