Deriving The Schwarzschild Solution - Alternative Form in Isotropic Coordinates

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:

. . .

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