cmb said:
I'm unconvinced. Why would people stick with "Newtonian Gravity" if there was something better to use?
Surely GR is not 'sooooo' complicated that it is impossible to model it (instead of "Newtonian gravity"). Is that what you are trying to say?
Thanks for your contribution but I can't follow your point. If you have some relevant reference confirming your assertion, that would be helpful.
The basic problem is that there isn't a literature out there of really rigorous analysis of GR minus Newtonian gravity in galaxy scale systems. There is back of napkin rough estimates making lots of spherical cow type assumptions, but there isn't much literature quantifying the magnitude of the non-linear effects of GR in non-spherical systems of galaxy scale. They are clearly not zero and haven't been rigorously bounded.
This isn't entirely a coincidence.
There is a statement in the Misner, Thorne and Archibald Gravitation textbook which implies that no observable effects arise from self-interactions of gravitational fields, which is almost surely an overstatement, and leaves people with an overstated impression of what is being said.
There have also been a number of papers looking at different non-linear GR effect (like gravitomagnetism) that don't work and have been rejected.
There is also the look for you keys under the lamp post effect. It is much, much easier to do Newtonian approximations, and it is much much easier to model GR effects in the spherically symmetric case in which the effect the Deur is interested in cancels out due to symmetry considerations.
Doing hard work to find something with a low Baysean probability of working out isn't the most attractive course of action.
I'd also note that another possibility is that Deur is indeed actually using equations that for subtle reasons are not actually standard Einstein equation GR (as he has asserted that they are). But suppose that is the case.
The equations still reproduce dark matter and dark energy and early structure phenomena. They reproduce MOND in disk galaxies and solve the insufficiency of dark matter phenomena in galactic clusters. They make novel observational predictions that have been confirmed that aren't found in other modified gravity theories. And, they manifestly reduce to the weak field Newtonian approximation (in a manner naturally generalized to be relativistic) on their face below a threshold that corresponds to the MOND constant. These equations do all of these things with a single field, not the scalar-tensor or scalar-vector-tensor fields that many other relativistic modified gravity theories require. These equations do all of these things without particle dark matter and without a cosmological constant of a substance to provide dark energy. This is still a very good day's work.
So, even if he is mistaken and he is not actually doing exactly Einstein's GR, if he has a versatile set of equations that can reproduce the phenomenology of both dark matter and dark energy, not just dark matter as MOND does, over a much wide range of applicability than MOND, in a quite simple and elegant way. Thus, whatever he has done to subtly modify Einstein's GR may be an accurate description of nature, and Einstein's GR may not be quite the right description of how gravity really acts in the infrared in systems that aren't spherically symmetrical. Whether or not it is truly faithful to Einstein's GR is something of an academic question if it works better to describe the universe.
After all, it's a dirty little secret but GR theorists actually have several different slight variations of GR on offer already that differ in subtle ways that aren't currently experimentally or observationally testable, such as teleparallel gravity, Einstein-Gauss-Bonnet, Einstein-Cartan theory, metric-affine gravity, etc. So, it really wouldn't be all that remarkable if the correct theory was a subtle tweak from the original 1917 version.