International Journal of Theoretical Physics

, Volume 53, Issue 6, pp 1971–1977 | Cite as

Equivalence Between an Extension of Teleparallelism to a Weyl Geometry and General Relativity

  • J. B. Formiga


Recently, an extension of teleparallelism to a Weyl geometry which allows us to easily establish conformal invariance and “geometrize” electromagnetism has been presented. In this paper, I extend a result which concerns the existence of the Schwarzschild solution to a particular class of this extension. In addition, I obtain the field equations of some models based on this extension, including the one which is equivalent to Einstein’s field equations with a massless scalar field.


Teleparallelism Weyl geometry Schwarzschild solution 


  1. 1.
    Capozziello, S., Faraoni, V.: Beyond Einstein Gravity: A Survey of Gravitational Theories for Cosmology and Astrophysics. Fundamental Theories of Physics. Springer, Dordrecht (2011) Google Scholar
  2. 2.
    Hehl, F.W., et al.: Phys. Rep. 258, 1 (1995) ADSCrossRefMathSciNetGoogle Scholar
  3. 3.
    O’Raifeartaigh, L.: The Dawning of Gauge Theory. Princeton Series in Physics. Princeton University Press, Princeton (1997) MATHGoogle Scholar
  4. 4.
    Sauer, T.: Hist. Math. 33, 399 (2006). arXiv:physics/0405142 CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Obukhov, Y.N., Pereira, J.G.: Phys. Rev. D 67, 044016 (2003) ADSCrossRefMathSciNetGoogle Scholar
  6. 6.
    Formiga, J.B., Fonseca Neto, J.B., Romero, C.: Phys. Rev. D 87, 067702 (2013) ADSCrossRefGoogle Scholar
  7. 7.
    Formiga, J.B.: Phys. Rev. D 88, 068501 (2013) ADSCrossRefGoogle Scholar
  8. 8.
    Hayashi, K., Shirafuji, T.: Phys. Rev. D 19, 3524 (1979) ADSCrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Wyman, M.: Phys. Rev. D 24, 839 (1981) ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    Formiga, J.B.: Phys. Rev. D 83, 087502 (2011) ADSCrossRefGoogle Scholar
  11. 11.
    Maluf, J.W.: Phys. Rev. D 67, 108501 (2003) ADSCrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Centro de Ciências da NaturezaUniversidade Estadual do PiauíTeresinaBrazil

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