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**[Moderator's note: this thread is spun off from another thread since it was a subthread dealing with a separate topic.]**

But strictly speaking, the maximally extended spacetime has another exterior region, so the full spacelike surface is actually two paraboloids joined at the ##r = 2M## surface. There is no "hole in spacetime" at ##r = 2M##.

There is definitely a maximally extended spacetime but there is no maximally extended spacelike surface of constant Schwarzschild coordinate time t. The spatial curvature (which is coordinate dependent) is infinite at r=2M.

It seems things are conflated here!

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