  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 only if the Higgs field has a particular radial profile,
S(r)=S_0 a/(r+a), decreasing from S_0 at r=0 with radial scale length a. Since
particle rest masses scale with S(r)/S_0, their world lines do not follow
time-like geodesics of the MK metric g_ab, as previously assumed, but rather
those of the Higgs-frame MK metric Omega^2 g_ab, with the conformal factor
Omega(r)=S(r)/S_0. 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.
