On reading Steve Giddings’s article, I felt the need to share some information about the original work of Karl Schwarzschild.
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His solution contained no coordinate singularity; it had only the singularity at the origin. That was neither a mistake nor an oversight on Schwarzschild’s part. By choosing a nontrivial scaling factor for the angular part of the metric, he had carefully avoided producing the coordinate singularity. As a side effect, such a choice results in a nonzero surface area for a sphere of zero radius. However, that result should not be a problem since one is not dealing with flat space anyway.
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