Singularities in Schwarzchild space-time

Can anyone explain when a co-ordinate and geometric singularity arise in Schwarzschild space-time with the element

$$ds^{2}~=~(1-\frac{2GM}{r})(dt)^{2}-(1-\frac{2GM}{r})^{-1}(dr)^{2}-r^{2}(d\theta)^{2}-(r^{2}\sin^{2}\theta)(d\theta)^{2}$$

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First of all: where are the singularities? You should be able to do that already. Then we can work out whether they are coordinate vs. geometric. –  Michael Brown May 1 '13 at 13:57
Is the singulatiry when the coeficient goes to $\infty$ so at r=0 and at infinity? –  user21119 May 1 '13 at 14:06
If you set $M=0$ you get a flat spacetime metric. That shows that there is no singularity at $r=\infty$, even though $g_{\theta\theta}=\infty$ there. Also, you're missing the place where $g_{rr}$ blows up. –  Ben Crowell May 1 '13 at 15:04
Hi user21119: did you check the Wikipedia page? –  Qmechanic May 1 '13 at 16:16
yeah thx, so would it be r=0 geometric and then r=2GM co-oridante –  user21119 May 2 '13 at 9:41