Conformal gravity rotation curves with a conformal Higgs halo
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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.
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
Monthly Notices of the Royal Astronomical Society
© 2016 The Author. Published by Oxford University Press on behalf of the Royal Astronomical Society. This work is made available online in accordance with the publisher’s policies. This is the final published version of the work, which was originally published at: https://dx.doi.org/10.1093/mnras/stw506
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