I was wondering, when sims of galaxies show that we need dark matter to account for the movement of outer stars, are models taking into account relativistic effects on gravity? The tips of spiral arms are causally shadowing gravity from the central bulk, as well as experiencing time at differing rates.
We don't think we need dark matter because of "sims" -- the evidence comes from more basic comparisons between orbital speeds and enclosed mass. When the discrepancies are factors of two or more (i.e., when the enclosed mass is $< 50$% of what would be needed to keep the stars, gas clouds, or galaxies in the system gravitationally bound, given how fast they are observed to be moving), tiny effects like relativistic time delays don't matter. Simulations might refine your estimates a little, but they won't change the basic conclusion.
In galaxy simulations, the relativistic time delays are not taken into account, because they are too small to matter. To see this, you need to realize that the mass distribution within galaxies changes on timescales of millions to billions of years. For example, the rotation period of the Milky Way's bar is about 100 million years, and the period of the Sun's orbit is more than 200 million years. These are several orders of magnitude larger than the relativistic time delays, so assuming there's zero time delay (as the simulations implicitly do) makes no practical difference at all.