4 HUBERT L. BRAY Figure 3. NGC3310 on the left, simulation on the right. The simulated image on the right results from running the Matlab func- tion spiralgalaxy(1, 75000, 1, -0.15, 2000, 1990, 100000000, 8.7e-13, 7500, 5000, 45000000, 50000) described in section 5.5. Left photo credit: NASA and The Hubble Heritage Team (STScI/AURA). Acknowledgment: G.R. Meurer and T.M. Heckman (JHU), C. Lei- therer, J. Harris and D. Calzetti (STScI), and M. Sirianni (JHU). Dates: March 1997 and September 2000. Telescope: Hubble Wide Field Planetary Camera 2. So, does the Klein-Gordon equation accurately describe dark matter and predict some observed properties and structures of galaxies? In this paper we present evidence of this possibility by trying to understand the effect that this model of dark matter would have on the structure of galaxies, which is a reasonable idea since galaxies have large components of dark matter. In doing so we have had to make approximations and educated guesses, so the comparisons in figures 1-6, while encouraging, should be taken in this context. Also, our “simulations” of galaxies only simulate the effect of the dark matter on the regular matter and hence are very primitive. Perhaps a better name would be “numerical experiments.” However, one has to start somewhere, and it is already interesting that compelling patterns very much resembling actual galaxies have emerged. We will describe the models we have used in sections 4, 5, and 6 and the assumptions we have made. We will do our best to clearly label where we have had to make approximations and educated guesses, as well as rigorous arguments, so that readers may make their own judgments about what is presented here. 2. Geometric Motivation Einstein’s theory of general relativity was made possible by Gauss and Rie- mann who, decades before, began the field of mathematics now called differential geometry. Since then, advances in differential geometry have played a crucial role in understanding the implications of Einstein’s theory. Einstein used differential geometry to make the qualitative statement “matter curves spacetime” precise,

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