Galaxy rotation curves incorporating relativistic mass and comparison with Keplerian velocity curves

We derive a formula for the velocity distribution of an axially symmetric galaxy where the mass density is corrected using the mass formula from special relativity. We take some reasonable test mass densities and numerically compute the resulting galaxy rotation curves. We then compare these to the rotation curves obtained from a similar formula without a relativistic correction factor. We find that the correction factor has a small dark-matter like effect. Finally, we compare these to the corresponding Keplerian velocity curves. We find that there is a large discrepancy in this case, where away from the galactic center, up to the galactic edge, the curves computed using our formulas give a noticeably higher velocity.