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In my notation above [itex]\gamma[/itex] is the gravitational constant. Let me know if you have serious comments.This is incorrect; there is no relativistic [itex]\gamma[/itex] factor in the formula for the Schwarzschild radius. The correct formula is

[tex]r_{s} = \frac{2 G m}{c^{2}}[/tex]

where [itex]G[/itex] is Newton's gravitational constant.