Apologies from earlier in the thread go to whoever I was arguing with over singularities.
Forgive me for forgetting all my mathematics.
Although the Event Horizon is also a singularity, just a removable one.
(Maths to follow for those of you who like this kind of thing)
The eqn we're looking at is
g^11 = (-1)/(1-2:lambda:/r)
Obviously, you'll get a singularity at r=2:lambda:, but this can be removed by an appropriate coordinate transformation and is designated as such.
In fact, r=2:lambda: gives us the location of the event horizon, but we can leave that aside at the moment.
The other interesting case is that g^11 => 0 as r => 0.
This seems perfectly trivial, until you consider that space time curvature is by the double differential of that equation (with respect to r), and so you find that
curvature ~ :lambda:/r^3, which will, when r=0, give infinite space time curvature as was said earlier in the thread.
ps.
It was faf I was arguing with, although his question 'What is the mass of a singularity?' is entirely pointless.
This reply sponsored by Mathematical Methods for Physics and Engineering by Riley, Hobson and Bence for reminding my ignorant brain of what a singularity is.