I think they should be the same (and I assume one could show this from the equation for gravitational time dilation). I haven't tried it but I think if you apply the Lorentz transform to the equation for escape velocity (which is the same as the speed when falling from infinity, which is your 11.186km/s) then you should end up with the equation for gravitational time dilation. Because equivalence. There is a big difference between not being refuted on an Internet forum and being mainstrea
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