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We revisit the structure of conformal gravity in the presence of a c-number,conformally coupled, long range, macroscopic scalar field. And in the static,spherically symmetric case discuss two classes of exact exterior solutions, inone of which the scalar field has a constant value and in the other, which isdue to Brihaye and Verbin, it has a radial dependence. In light of these twosolutions Horne and then Hobson and Lasenby raised the concern that the fittingof conformal gravity to galactic rotation curves had been misapplied and thuscalled the successful fitting of the conformal theory into question. We showthat the analysis of Brihaye and Verbin is not actually general, but isnonetheless valid in the particular case that they studied. For the analyses ofHorne and of Hobson and Lasenby we show that this macroscopic scalar field isnot related to the mass generation that is required in a conformal theory.Rather, not just in conformal gravity, but also in standard Einstein gravity,the presence of such a long range scalar field would lead to test particleswhose masses would be of the same order as the masses of the galaxies aroundwhich they orbit. Since particle masses are not at all of this form, suchmacroscopic fields cannot be responsible for mass generation; and the existenceof any such mass-generating scalar fields can be excluded, consistent withthere actually being no known massless scalar particles in nature. Instead,mass generation has to be due to c-number vacuum expectation values of q-numberfields. Such expectation values are microscopic not macroscopic and only varywithin particle interiors, giving particles an extended, baglike structure, asneeded for localization in a conformal theory. And being purely internal theyhave no effect on galactic orbits, to thus leave the good conformal gravityfitting to galactic rotation curves intact.

Structure of conformal gravity in the presence of a scale breaking scalar field