On Wave Dark Matter, Shells in Elliptical Galaxies, and the Axioms of General Relativity

This paper is a sequel to the author’s paper entitled “On Dark Matter, Spiral Galaxies, and the Axioms of General Relativity” which explored a geometrically natural axiomatic definition for dark matter modeled by a scalar field satisfying the Einstein-Klein-Gordon wave equations which, after much calculation, was shown to be consistent with the observed spiral and barred spiral patterns in disk galaxies, as seen in Figures 3, 4, 5, 6. We give an update on where things stand on this “wave dark matter” model of dark matter (aka scalar field dark matter and boson stars), an interesting alternative to the WIMP model of dark matter, and discuss how it has the potential to help explain the long-observed interleaved shell patterns, also known as ripples, in the images of elliptical galaxies. In section 1, we begin with a discussion of dark matter and how the wave dark matter model compares with observations related to dark matter, particularly on the galactic scale. In section 2, we show explicitly how wave dark matter shells may occur in the wave dark matter model via approximate solutions to the Einstein-Klein-Gordon equations. How much these wave dark matter shells (as in Figure 2) might contribute to visible shells in elliptical galaxies (as in Figure 1) is an important open question.