Help with showing the existance of the Schwarzschild singularity at r=0.

[blp]

According to Wikipedia, if the metric was vacuum, spherically symmetric and static the Schwarzschild metric may be written in the form:
ds^2=((1-2GM/(c^2r))^-1)*dr^2+r^2*(dtheta^2+sin(theta)^2*dphi^2)-c^2*(1-2GM/(c^2r))*dt^2
I need someone to help me to derive an expression from the Schwarzschild metric that is a function of r that can be graphed, that clearly shows the singularity at r=0. Actually, their is apparently a pair of pos and neg singularities there. Is that true? Is that because there is a square root taken during it's derivation? Thanks.

 

[Mentz114]

Surely

$$1- \frac{2GM}{c^2r}$$ clearly diverges when r = 0. And its inverse diverges when

$$1 = \frac{2GM}{c^2r}$$.

 

[blp]

Sorry, I should have been clearer. Obviously ds^2 diverges at r=0, but I want some way of graphing a 2D spacetime clearly curving towards infinity in the z axis direction as r approaches 0.

Also concerning the pair of pos and neg singularities at r=0. I remember reading somewhere that shortly after Schwarzschild came up with the black hole solution to GR that Einstein and Rosen noticed the above pair of singularities and interpreted them as being the two ends of a wormhole and called it a Einstein-Rosen bridge. If that is true, I'm curious how the singularities were mathematically derived. Does anyone know?

 

[Mentz114]

I think space-times are analysed with Kruskal or Penrose diagrams. If you want to take an equatorial slice, then rewrite the metric in cartesian coordinates. I can't say any more than that, not having studied the singularites because I don't think they can be physical. But that's just an opinion.

 

[blp]

Thanks! I'm going to re post this with a different title to see if someone else might know about this.