# Has frame dragging been accounted for in galactic rotation curves?

This article explicitly takes frame dragging into account in calculating expected galactic rotation curves in the absence of dark matter, and appears to obtain very close matches to observed curves. Is it true that frame dragging is typically ignored in analysis of galactic rotation curves? If so, it seems like a huge oversight.

• Frame dragging is a small effect, suppressed by order $v^2/c^2$ relative to the gravitational attraction. For objects in the galaxy, $v/c \sim 10^{-3}$, so the effect is order $10^{-6}$ which is far too small. Mar 6, 2021 at 3:29
• The paper has probably just screwed up some step of the analytic argument, resulting in a massive overestimation of the effect. That's what happens when you hyper-focus on solving differential equations exactly, getting a forest of special functions, without ever doing a back of the envelope check. Mar 6, 2021 at 3:30
• Furthermore, there have been lots of papers on adding general relativistic corrections to $N$-body simulations... the only reason you haven't heard much about them is because everybody already knows it's a technical point that will provide small corrections. It's not like everybody forgot general relativity is a thing! Mar 6, 2021 at 3:40
• ^^^ that. should be the answer (preceded by a "yes") rather than just a comment ;)
– rfl
Mar 6, 2021 at 16:15
• That article seems to assume that bulk rotation of the stars (“mass currents”) is key, as though all galaxies are spiral galaxies, but this ignores all the evidence for dark matter in non-rotating galaxies. Jun 10, 2021 at 12:45

Frame dragging is a small effect, suppressed by order $$v^2 / c^2$$ relative to the gravitational attraction. For objects in the galaxy, $$v/c \sim 10^{-3}$$, so the effect is of order $$10^{-6}$$, which is far too small to make a noticeable difference. The other uncertainties are far greater than that.

That paper has probably just screwed up some step of the analytic argument, resulting in a massive overestimation of the effect. That's what happens when you hyper-focus on solving differential equations exactly, getting a forest of special functions, without ever doing a back of the envelope check. Unfortunately, it has received far more attention than it deserves, because of a lot of uncritical news articles.

• At least one person claims to have identified the specific error in Ludwig's paper dispatchesfromturtleisland.blogspot.com/2021/04/… Aug 14, 2021 at 4:36
• @MitchellPorter I'm not surprised Lisi came to the same conclusion about this paper, it's basic GR! I'm also glad he tweeted about it, because the problem with these kinds of papers is they tend to go uncritically accepted on the internet at large. I write a little Physics.SE answer when needed but nobody ever sees it. Also thanks for the tip about Hanson's blog post. If I'm reading it correctly, that is a really glaring error. Aug 14, 2021 at 4:48
• @MitchellPorter Specifically, Ludwig seems to be treating stars as a pressureless fluid in static equilibrium held in place by gravitomagnetism, which is crazy. Stars are constantly in motion, they just fall through the galactic plane all the time! The right way to treat this kind of problem (which is again, textbook material, e.g. Binney and Tremaine) is to consider a stationary density on phase space, not on physical space. Aug 14, 2021 at 4:51

You can check this recent paper, that (hopefully) add a quite final point to the discussion of GR effects on the rotation curves of disk galaxies:

https://arxiv.org/pdf/2207.09736.pdf

The gravitomagnetic effect on the rotation curve of a disk galaxy model with realistic (i.e. exponentially declining) density profile is rigorously calculated. The corrections over the newtonian predictions are found of the order (v/c)^2 ~ 10^-6 over the whole disk, confirming standard GR expectations: GR and newtonian rotation curves are for all practical purposes identical, and DM is required in GR as in newtonian gravity.

Notice that the newtonian rotation curve of an exponential disk is almost flat up to ~ 3 scale-lenghts of the (visibile) stellar disk (already containing more than 80 per cent of the stars), so DM indications from rotation curves are NOT derived from rotation curves of stars. This is well known in astronomy since the '80: the only robust indications of DM in disk galaxies are obtained from the rotation curve in HI, well beyond the end of the visibile disk.

To predict a flat rotation curve of stars in a stellar disk by using GR is not resolving the problem of DM: quite the opposite, is just a confirmation (as expected) of the newtonian predictions.