This is very old hat, this idea that dark matter might not exist, might not be stuff at all but rather a flaw in General Relativity.

Various theories of modified gravity have been proposed to explain the discrepancy in the rotation of galaxies since it was observed (here's a wikipedia for MOND, a whole category of these theories that has been around for 40 years now: https://en.wikipedia.org/wiki/Modified_Newtonian_dynamics). Some of these modified theories explain galactic rotation quite well, have done so for decades!

The problem is that for many years now we have had additional evidence beyond galaxy rotation that suggests dark matter is "stuff," most famously the divergence of mass in the Bullet Cluster observed via gravitational lensing vs. that observed via light/radio/ir radiation. More recently, models in cosmology of the expansion of the universe require extra mass to explain the observed distribution of the cosmic microwave background.

This new paper does not explain any of this additional evidence suggesting the existence of dark matter as "real stuff," it only explains galactic rotations-- and there are piles of old theories lying around that can do that. There is no particular reason to regard any of them as more than overly clever mathematical exercises (until one comes along that makes a testable prediction; Ludwig's paper does not).

The only claim that Ludwig makes for his theory over MOND theories is that his explanation is non-Newtonian... fine for a bit of mathematical one-upmanship, I suppose, but it doesn't even predict any of the other observed phenomena commonly attributed to dark matter, let alone predict anything new to test.

1) did i tell you i post physics news just for your comments. this is true.

To borrow a quote:
Mr. Fisher, on Mount Wilson there is a telescope that can magnify the most distant stars up to twenty-four times the magnification of any previous telescope. This remarkable instrument was unsurpassed in the world of astronomy until the construction of the Mount Palomar telescope, an even more remarkable instrument of magnification. Owing to advances and improvements in optical technology, it is capable of magnifying the stars to four times the magnification and resolution of the Mount Wilson telescope - Mr. Fisher, if you could somehow put the Mount Wilson telescope inside the Mount Palomar telescope, you still wouldn't be able to detect my interest in your problem.”
George S. Kaufman

Wow robotslave, bask in that! (@2)

@4 It might be a bit more flattering if there were more than a handful of comments on Mudede science posts to begin with? But you're right, it's quite nice. Thank you, Charles.

@5:

If I thought I was in any way competent to respond to the article, I'd be more than happy to do so. But, as much as I love and support scientific enquiry, this particular subject is beyond my ken. So, all I can say is - huzzah to you, sir!