Abstract
In this study, we have investigated the geometrical and physical properties of stationary axisymmetric solutions. The expressions for the axial-vector and the gravitational energy and momentum densities are obtained in the context of teleparallel equivalent of general relativity. The obtained results are compared with that obtained previously in the context of Møller’s tetrad theory of gravitation. We discussed special cases of these solutions.
Similar content being viewed by others
Notes
Here the Greek indices μ,ν,λ,… have the range 0,…,3, and denote tensor indices, i.e. indices related to space-time; Latin indices a,b,c,…, have the range 0,…,3, will be used to denote local Lorentz (or tangent space) indices.
References
Aldrovandi, R., Pereira, J.G.: An Introduction to Geometrical Physics. World Scientific, Singapore (1995)
de Andrade, V.C., Pereira, J.G.: Phys. Rev. D 56, 4689 (1997)
de Andrade, V.C., Pereira, J.G.: Phys. Rev. D 56, 4689 (1998)
Hayashi, K., Shirafuji, T.: Phys. Rev. D 19, 3524 (1979)
Hehl, F.W., Lemke, J., Mielke, E.W.: Two lectures on fermions and gravity. In: Debrus, J., Hirshfield, A.C. (eds.) Geometry and Theoretical Physics. Springer, Berlin (1991)
Maluf, J.W.: J. Math. Phys. 35, 335 (1994)
Møller, C.: The Theory of Relativity. Clarendon, Oxford (1952)
Nashed, G.G.L.: Astrophys. Space Sci. 330, 173 (2010)
Nitsch, J., Hehl, F.W.: Phys. Lett. B 90, 98 (1980)
Pereira, J.G., Varags, T., Zhang, C.M.: Class. Quantum Gravity 18, 833 (2001)
Sharif, M., Amir, M.J.: Gen. Relativ. Gravit. 39, 989 (2007)
Stephan, H., Kramer, D., MacCallum, M.A.H., Heonselaers, C., Hearlt, E.: Exact Solutions of Einstein’s Field Equations. Cambridge University Press, Cambridge (2003)
Tupper, B.O.J.: Class. Quantum Gravity 1, 71 (1984)
Tupper, B.O.J.: Class. Quantum Gravity 2, 427 (1985)
Weitzenböck, R.: Invariantentheorie. Noordhoff, Groningen (1923)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Gad, R.M. On teleparallel version of stationary axisymmetric solutions and their energy contents. Astrophys Space Sci 346, 553–557 (2013). https://doi.org/10.1007/s10509-013-1476-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-013-1476-4