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MeJennifer
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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.]
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!
PeterDonis said: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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