Conformal gravity rotation curves with a conformal Higgs halo
Abstract
We discuss the effect of a conformally coupled Higgs field on Conformal Gravity (CG) predictions for the rotation curves of galaxies. The Mannheim-Kazanas (MK) metric is a valid vacuum solution of CG's 4-th order Poisson equation if and only if the Higgs field has a particular radial profile, S(r) = S0 a/(r + a), decreasing from S0 at r = 0 with radial scale length a. Since particle rest masses scale with S(r)/S0, their world lines do not follow time-like geodesics of the MK metric gμν, as previously assumed, but rather those of the Higgs-frame MK metric ḡμν = Ω2 gμν, with the conformal factor Ω(r) = S(r)/S0. We show that the required stretching of the MK metric exactly cancels the linear potential that has been invoked to fit galaxy rotation curves without dark matter. We also formulate, for spherical structures with a Higgs halo S(r), the CG equations that must be solved for viable astrophysical tests of CG using galaxy and cluster dynamics and lensing.
Citation
Horne , K D 2016 , ' Conformal gravity rotation curves with a conformal Higgs halo ' , Monthly Notices of the Royal Astronomical Society , vol. 458 , no. 4 , pp. 4122-4128 . https://doi.org/10.1093/mnras/stw506
Publication
Monthly Notices of the Royal Astronomical Society
Status
Peer reviewed
ISSN
0035-8711Type
Journal article
Collections
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