Alternative Form in Isotropic Coordinates
The original formulation of the metric uses anisotropic coordinates in which the velocity of light is not the same in the radial and transverse directions. A S Eddington gave alternative forms in isotropic coordinates. For isotropic spherical coordinates, coordinates and are unchanged, and then (provided r >= 2Gm/c2 )
. . ., . . ., and
. . .
Then for isotropic rectangular coordinates, ,
The metric then becomes, in isotropic rectangular coordinates:
. . .
Read more about this topic: Deriving The Schwarzschild Solution
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