Abstract
Light propagating through Dark Matter suffers gravitational frequency shifts. We derive the differential equation and its solution for spherical Dark Matter. This is then applied to condensed neutrino objects (CNO) which are a candidate for Dark Matter. The Local Group of Galaxies seems to be embedded within a CNO (Morley and Buettner in MDPI Universe 3(4):81, 2017), and we derive the gravitational frequency shift of light from M33 and M31 to the Milky Way. For a galaxy embedded in a general CNO, we present the link analysis of how the gravitational frequency shift is computed. In general, all these gravitational frequency shifts are small, even though CNO would be the largest and most massive Dark Matter in the Universe.
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KATRIN https://www.katrin.kit.edu.
CNO can be in aspherical normal modes of vibration due to the coupling of the CNO with the moving galaxies inside (Morley and Buettner 2016); we ignore this perturbation here.
We assume that the typical CNO has equal numbers of neutrinos and anti-neutrinos. Since these neutral leptons flavor mix, the CNO then has equal numbers of neutrino flavors and anti-neutrino flavors and a resulting one Fermi momentum.
In the computer program calculating the following numbers, full double precision accuracy was kept, but is not shown in the paper.
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Morley, P.D. Dark matter gravitational spectral shifts in the local group. Astrophys Space Sci 365, 57 (2020). https://doi.org/10.1007/s10509-020-03765-x
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DOI: https://doi.org/10.1007/s10509-020-03765-x