Thin-disk models in an integrable Weyl–Dirac theory

  • Ronaldo S. S. Vieira
  • Patricio S. Letelier
Research Article


We construct a class of static, axially symmetric solutions representing razor-thin disks of matter in the Integrable Weyl–Dirac theory proposed in Israelit (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 along 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 of 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 geometrical fields introduced by this theory.


Weyl–Dirac theory Exact solutions Galaxy astrophysics Modified gravity 



R.S.S.V. thanks Davi C. Rodrigues for helpful discussions about the astrophysics of galaxies, Mark Israelit for valuable comments on an earlier version of this manuscript and Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) for financial support. This work is dedicated to the memory of Prof. Patricio S. Letelier, who passed away after the elaboration of the first draft of this manuscript.


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© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Instituto de Física “Gleb Wataghin”Universidade Estadual de CampinasCampinasBrazil
  2. 2.Departamento de Matemática Aplicada-IMECCUniversidade Estadual de CampinasCampinasBrazil

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