Dear Christian,

I think these examples will help you, taking advantage of the relationship of Einstein's equations with Gaussian curvature, concepts and calculations are simplified:

http://dx.doi.org/10.13140/RG.2.2.19090.27846

Dear Christian Conkle,

" Possibility of using a reference frame to account for dark matter, or summing the kinetic energies in a galaxy?"

Dark Matter is a fantasy according to my published research. And yes, that's what's missing from our understanding concerning the rotation anomalies of spiral galaxies, an alternative reference frame. There is a rotating background field of non-matter particulates, aka an aether of sorts, within spiral galaxies that should be viewed as a preferred reference frame. It's motion can be exactly calculated only using the observable galactic matter. When this fields' calculated motion is subtracted out from the observed motion, we have exactly calculated the stellar velocities within these spiral galaxies. The only data needed is the amount and radial locations of the observed galactic matter. The results are statistically exact.

The same explanation applies to galaxies in a cluster, the excess bending of light, and most everything else now attributed to the effects of dark matter. The paper itself shows such exact calculations. No kinetic energy calculations are needed. It's far simpler than that, according to our conclusions.

It's a fairly long research paper, 4 years in the making. If you want the entire preprint I'll send it to you you via e-mail : [email protected]

https://scholar.google.com/citations?user=7ONCj-kAAAAJ&hl=en#d=gs_md_cita-d&u=%2Fcitations%3Fview_op%3Dview_citation%26hl%3Den%26user%3D7ONCj-kAAAAJ%26citation_for_view%3D7ONCj-kAAAAJ%3Ad1gkVwhDpl0C%26tzom%3D480

Hi Christian,

please be aware, that dark matter is the most widely accepted theory at the moment.

Let me first point out that Gravitation is viewed as a deformation of space time. That means we are living in a 4 dimensional world with 3 spacial and one time dimension. This Space is deformed by Energy. This includes mass, but also other types.

In Cosmology we see from the Bullet Cluster or Gravitational Lensing ( light being bent by gravity towards our planet, so we can observe it) that there is a gravitational effect, our current proven theories are not able to explain. The best explanation we have at the moment is that we are seeing gravitational effects of matter, which was not yet observed.

A good starting point in order to understand this better is actually wikipedia:

For GR:

https://en.wikipedia.org/wiki/Introduction_to_general_relativity

which provides a list of several resources I would recommend you to look into, if you are interested in this. In particular reference 20 (A simple explanation of mass–energy equivalence can be found in sections 3.8 and 3.9 of Giulini 2005.) should give a satisfactory answer to your question I think.

Further more, if you are interested to learn more about GR have a look at this book:

Einstein Gravity in a Nutshell (Princeton University Press) from A. Zee

The mass associated to kinetic energy is negligible in a galaxy, or in galaxy cluster, in regard of the rest mass at the source of Newtonian or Einsteinian gravity. The relative additional mass caused by kinetic energy is of order (v/c)^2, where v is the average (virial) velocity and c the speed of light. Most galaxies have a v in the interval 50-350 km/s and in galaxy clusters 200-1500 km/s, in regard of 300'000 km/s for c. For galaxies those with most dark matter fraction have a low v, so dark matter anticorrelates with v.