Thin-disk models in an Integrable Weyl-Dirac theory

We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in an Integrable Weyl-Dirac theory proposed in Found. Phys. 29, 1303 (1999). The main differences between these solutions and the corresponding general relativistic one are analyzed, focusing on the behavior of physical observables (rotation curves of test particles, density and pressure profiles). We consider the case in which test particles move on Weyl geodesics. The same rotation curve can be obtained from many different solutions of the Weyl-Dirac theory, although some of these solutions present strong qualitative differences with respect to the usual general relativistic model (such as the appearance a ring-like density profile). In particular, for typical galactic parameters all rotation curves of the Weyl-Dirac model present Keplerian fall-off. As a consequence, we conclude that a more thorough analysis of the problem requires the determination of the gauge function $\beta$ on galactic scales, as well as restrictions on the test-particle behavior under the action of the additional fields introduced by this theory.