Teleparallel formalism of Galilean gravity

S.C. Ulhoa1, F.C. Khanna2, A.E. Santana3


A pseudo-Riemannian manifold is introduced, with light-cone coordinates in (4+1)-dimensional space-time, to describe a Galilei covariant gravity. The notion of 5-bein and torsion are developed, and a Galilean version of teleparallelism is constructed in this manifold. The formalism is applied to two spherically symmetric configurations. The first one is an ansatz which is inferred by following the Schwarzschild solution in general relativity. The second one is a solution of Galilean-covariant equations. In addition, this Galilei teleparallel approach provides a prescription for coupling of the 5-bein field to the Galilean-covariant Dirac field.


  1. M. de Montigny, F. C. Khanna, and F. M. Saradzhev, Annals Phys. 323, 1191 (2008), arXiv: 0706.4106.
  2. N. C. T. Coote and A. J. Macfarlane, Gen. Rel. Grav. 9, 621 (1978).
  3. M. Kobayashi, M. de Montigny, and F. C. Khanna, J. Phys. A 41, 125402 (2008), arXiv: 0710.5556.
  4. R. d'Inverno, Introducing Einstein's Relativity, 4th ed. (Clarendon Press, Oxford, 1996).
  5. L. D. Landau and E. M. Lifshiz, The Classical Theory of Fields, 4th ed., Course of Theoretical Physics, Vol. 2 (Elsevier Butterworth-Heinemann, 2004).
  6. R. Aldrovandi, J. G. Pereira, and K. H. Vu, Braz. J. Phys. 34, 1374 (2004), gr-qc/0312008.
  7. J. Maluf, S. Ulhoa, F. Faria, and J. da Rocha-Neto, Class. Quantum Grav. 23, 6245 (2006).
  8. J. W. Maluf, Annalen Phys. 14, 723 (2005), gr-qc/0504077.
  9. F. W. Hehl, J. D. McCrea, E. W. Mielke, and Y. Ne'eman, Metric-affine Gauge Theory of Gravity: Field Equations, Noether Identities, World Spinors, and Breaking of Dilation Invariance (1994).
  10. F. W. Hehl, J. Lemke, and E. W. Mielke, in: Geometry and Theoretical Physics, ed. by J. Debrus and A. C. Hirshfeld (Springer, Berlin, 1991).
  11. R. Cuzinatto, P. Pompeia, M. de Montigny, and F. Khanna, Phys. Lett. B 680, 98 (2009).
  12. S. C. Ulhoa, F. C. Khanna, and A. E. Santana, Int. J. Mod. Phys. A24, 5287 (2009), arXiv: 0902.2023.
  13. E. S. Santos, M. de Montigny, F. C. Khanna, and A. E. Santana, J. Phys. A: Math. Gen. 37, 9771 (2004).
  14. F. C. Khanna, A. E. Santana, A. Matos Neto, J. D. M. Vianna, and T. Kopf, hep-th/9812222.
  15. D. T. Son, Phys. Rev. D 78, 046003 (2008).
  16. K. Balasubramanian and J. McGreevy, Phys. Rev. Lett. 101, 061601 (2008).
  17. C. R. Hagen, Phys. Rev. D 5, 377 (1972).
  18. Y. Nishida and D. T. Son, Phys. Rev. D 76, 086004 (2007).
  19. Y. Brihaye, C. Gonera, S. Giller, and P. Kosinski, hep-th/9503046.
  20. M. de Montigny, F. C. Khanna, A. E. Santana, and E. S. Santos, J. Phys. A: Math. Gen. 34, 8901 (2001).
  21. A. Harindranath, L. Martinovic, and J. P. Vary, Phys. Rev. D 62, 105015 (2000).
  22. N. C. J. Schoonderwoerd and B. L. G. Bakker, Phys. Rev. D 58, 025013 (1998).
  23. N. C. J. Schoonderwoerd and B. L. G. Bakker, Phys. Rev. D 57, 4965 (1998).
  24. N. E. Ligterink and B. L. G. Bakker, Phys. Rev. D 52, 5954 (1995).
  25. J. Beckers and M. Jaspers, Physica A: Statistical and Theoretical Physics 79, 338 (1975).
  26. J. B. Kogut and D. E. Soper, Phys. Rev. D 1, 2901 (1970).
  27. L. Susskind, Phys. Rev. 165, 1535 (1968).
  28. D. Flory, Phys. Rev. D 1, 2795 (1970).
  29. S. Weinberg, Phys. Rev. 150, 1313 (1966).
  30. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-Particle Systems (Dover Publications, 2003).
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page