"The Alternative to Dark Matter May be General Relativity Itself"

From Astrobites. Here are the highlights:

For most astronomers, it is just common sense that dark matter accounts for approximately 85% of the matter in the universe. However, as long as the constituents of dark matter remain a mystery, some astronomers remain skeptical about our conventional understanding of dark matter. Recently, astronomer Alexandre Deur suggested that the theory of relativity itself may explain a phenomenon widely regarded as evidence for dark matter...

Modified Newtonian Dynamics, or MOND, for example, is the most discussed out of all the gravitation corrections to explain the missing mass problem (see this astrobite for further discussion of MOND vs. dark matter). It modifies the Newtonian gravitation law at low accelerations to enhance the effective gravitational attraction. Similarly, most of the other corrections require new descriptions of gravitation. But recently, as Deur proposes in this work, the effect of general relativity may account for the missing mass, without introducing any new corrections.

Yes, MOND is a bit of a fudge and an approximation, but the general approach is correct. It's a lot less of a fudge than inventing Dark Matter.

Generally, the predicted rotation of galaxies, as shown in Figure 1, is modelled by Newtonian dynamics. The rotation velocity is much smaller than the speed of light, especially at the outer part of the galaxy (typically v/c ≈ 0.1 % , where v is the velocity and c is the speed of light). Therefore, it is believed that a non-relativistic treatment is reasonable. However, this assumption could be challenged due to the effect of field self-interaction in general relativity. This effect depends on the mass only, and is independent of the rotation velocity, thus making a difference regardless of how fast the stars move in the galaxy. Deur shows that field self-interaction, which reveals the non-linear nature of general relativity, is in fact not negligible in the missing mass problem.

To demonstrate this, Deur uses the gravitational lensing formalism. While light travels in straight lines in flat space, it can be deflected in the presence of a gravitational field. In exactly the same way, the gravitational field lines connecting two parts of the galaxy are distorted by the background field. That is to say, the gravitational field is deformed by the total galactic mass. With the field lines distorted, the strength of the gravitation consequently changes.

Yup, gravity lenses itself, i.e. it focuses itself on the mass that created the gravity in the first place. You can guess this for yourself. Once they have worked out how and to what degree, they'll hopefully show that there was no need to invent Dark Matter, and the concept will be quietly shelved.