Dear Chris,
Thanks so much for reading my essay - and especially your kind remarks!
I understand (in principle) that general relativity is fundamentally more accurate than classical physics and at least more correctly and more completely describes the physical effects of gravitation. However, I must take exception to the statement that "The existence of Dark Matter is admitted in order to justify Newtonian theory." IMO, a more correct statement would be that 'The existence of Dark Matter is admitted in order to justify the misapplication of overly-simplistic methods of approximation based on pre-Newtonian physics.'
Reading your paper, "High-energy scalarons in R^2 gravity as a model for Dark Matter in galaxies" (which I found very interesting, to the extent that I could comprehend), I think I should explain that, in my view, the fundamental issue with galaxy gravitational evaluations is not (when correctly applied) Newtonian physics, it is the expedient misapplication of even simpler methods of approximation by astronomers and others. There are several references to research in my 'Supplemental Info." and "Cited Works" sections (the latter correcting one erroneous URL) that more correctly represent galactic mass configurations using Newtonian dynamics and gravitation to successfully represent observed galaxy rotation. There is also a reference using general relativity - Fred Cooperstock also takes the view that the failing is inherent in Newtonian physics.
In my information systems analyst view, the application overly-simplistic methods of gravitational approximation to more complex structures introduces scale variant errors in the estimation of both non-luminous masses and the effects of gravitational interactions among discrete objects within very large composite structures. As I think is inherent in gravitational evaluation methods prescribed in general relativity, galactic disks are self-gravitating aggregations of massive objects, avoiding at least the errant evaluation of gravitational effects.
I have a lot of thoughts regarding gravitational lensing effects attributed to dark matter, especially through the compound lens that must be presented by galaxies within galaxy clusters. While certainly a 'localized' large scale structure such as a galaxy cluster must produce a collective curvature of spacetime, each relatively compact galaxy must also produce a more intensive, if more localized, curvature of spacetime. I suspect that generalizing the magnitude of lensing effects produced to consider only the overall structure in order to facilitate evaluation may introduce large scale errors into the results. I think (not comprehending math) I may have detected some perhaps over-generalizations in your equations - is that possible?
I've had some very long and tedious discussions with Peter Jackson attempting to explain that the Bullet Cluster's separation of gas and non-interacting masses does falsify his assertion that ionized gasses produce the effects attributed to dark matter. While I agree with him that non-detectable gasses represent an under-appreciated quantity at all scales, the decelerated gasses comprising intracluster media apparently cannot produce galaxy cluster lensing effects.
I think it's much more telling that dark matter is almost always coincidentally located with galaxies. Perhaps, in a literary sense, it is dark matter that cannot exist without galaxies! I think the method often used to estimate 'ordinary' galaxy mass based on luminosity is a perfect fit for main sequence stars, whose mass directly produces luminosity. However, applying that method to galaxies generally ignores a significant independently contributing factor of non-numinous (and often luminosity obscuring disperse) masses. As I understand, it's generally resulted in spiral galaxies often requiring large amount of compensatory dark matter - they also contain relatively large volumes of dust and gas. This, in conjunction with simplified methods of approximating gravitation relying too much on a compound object's center of mass and not considering the effects of so many discretely interacting objects, often produces underestimated masses for large scale composite masses.
To conclude all of this, I think that if the original requirement truly establishing the existence of dark matter in galaxies was a product of improper analysis, as I think I've established, and galactic rotation can be explained in the context of existing physics, then it should follow that galactic dark matter does not exist, at least in significant amounts. While I agree that this does not preclude its existence throughout the rest of the universe, I think that cosmologists rely entirely on galactic dark matter estimates for their presumptive universal proportion of dark matter to 'ordinary' matter. To that extent, if there's no requirement for galactic dark matter it should follow that there's no justification for cosmological dark matter, no matter how expedient it might be for cosmological analyses. At least that's the way this information systems analyst sees it...
Thanks again, Jim
