Effects of dark matter

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.

• People have tried all sorts of schemes to avoid dark matter. They don't work. If they succeed in getting galaxy rotation curves right, they fail in something else, eg gravitational lensing. But what do you mean by "shadowing gravity"? Consider: during a lunar eclipse, the Earth doesn't shadow the Moon from the Sun's gravity, only from its light. If gravitational shadowing happened, it'd have an obvious effect on the Moon's orbit. – PM 2Ring Feb 8 '19 at 23:51
• Shadowing gravity in the sense that, for our galaxy, gravity from the central bulk of the bar doesn't reach the tips of the spiral arms for about 40k years. – Samuel Rawlings Feb 9 '19 at 0:46
• EDIT Shadowing gravity as in causally delayed, in the sense that, for our galaxy, gravity from the central bulk of the bar doesn't reach the tips of the spiral arms for about 40k years. For matter half way along that spiral arm it would take 20k years for gravity to reach the tips, and so on. Are our simulations of galactic rotation taking into consideration the delayed nature of gravity reaching the tips of the spiral arms from the bulk of the core? It strikes me that the very nature of arms that spiral is due to of the speed of causality. The further the arms reach, the more they spiral – Samuel Rawlings Feb 9 '19 at 0:55
• We have 100k LY across galaxy. It takes 50k years for grav from the bulk to reach outer arms. Grav from stars 25k LY away from the bulk take 25kY to reach the tips of the arms & core. Grav from stars 90k years from the core reach the tips at 10k years, while still 90k years away from the bulk. We have not properly encoded relativistic effects in to galactic grav sims. We could test this. Galaxies with fast orbits of far stars will appear to have more “dark matter” than those with closer/slower orbits. Galaxies with slow/no rotation will have little/no “dark matter” – Samuel Rawlings Feb 9 '19 at 2:58
• @SamuelRawlings I did not understand how the delayed gravitational effect would change the velocity of the outer spiral ? – Layla Feb 9 '19 at 7:52

1. 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.