Abstract
We apply the energy-momentum tensor which is coordinate independent, of the gravitational field established in the Hamiltonian structure of the teleparallel equivalent of general relativity (TEGR), to an axially symmetric tetrad field to calculate energy, momentum and angular momentum. Also the definition of the gravitational energy is used to investigate the energy within the external event horizon of this tetrad.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aguiregabiria, J.M., Chamorro, A., Virbhadra, K.S.: Gen Relativ. Gravity 28, 1393 (1996)
Arnowitt, R., Deser, S., Misner, C.W.: Gravitation: An Introduction to Current Research (edited by L. Witten). Wiley, New York (1962)
Ashtekar, A.: Angular momentum of isolated systems in general relativity. In: Bergmann, P.G., de Sabbata, V. (eds.) Cosmology and Gravitation. Plenum, New York (1980)
Baekler, P., Hehl, F.W.: (2006). gr-qc/0601063
Bergmann, P.G., Thomson, R.: Phys. Rev. 89, 401 (1953)
Blagojević, M.: Gravitation and Gauge Symmetries. IOP Publishing, Bristol (2002)
Blagojević, M., Nikolić, I.A.: Phys. Rev. D 62, 024021 (2000)
Blagojević, M., Vasilić, M.: Class. Quantum Gravity 5, 1241 (1988)
Blagojević, M., Vasilić, M.: Class. Quantum Gravity 17, 3785 (2000)
Brans, C., Dicke, R.H.: Phys. Rev. 124, 925 (1961)
de Andrade, V.C., Pereira, J.G.: Phys. Rev. D 56, 4689 (1997)
Dirac, P.A.M.: Lectures on Quantum Mechanics. Belfer Gradute School of Science Monographs Series, vol. 2. Yeshiva University, New York (1964)
Gronwald, F., Hehl, F.W.: On the gauge aspects of gravity. In: Bergmann, P.G., et al. (eds.) International School of Cosmology and Gravitation 14th Course: Quantum Gravity, Held May 1995 in Erice, Italy, Proceedings. World Scientific, Singapore (1996). gr-qc/9602013
Hayashi, K.: Phys. Lett. B 69, 441 (1977)
Hayashi, K., Shirafuji, T.: Phys. Rev. D 19, 3524 (1979)
Hayashi, K., Shirafuji, T.: Prog. Theor. Phys. 73, 54 (1985)
Hehl, F.W.: Four Lectures on Poincaré gauge theory. In: Bergmann, P.G., De Sabbata, V. (eds.) Proceedings of the 6th School of Cosmology and Gravitation Course on Spin, Torsion Rotation and Supergravity, held at Eric, Italy (1979). Plenum, New York (1980)
Hehl, F.W., Neeman, Y., Nitsch, J., Von der Heyde, P.: Phys. Lett. B 78, 102 (1978)
Hehl, F.W., MacCrea, J.D., Mielke, E.W., Ne’eman, Y.: Phys. Rep. 258, 1 (1995)
Itin, Y.: Class. Quantum Gravity 19, 173 (2002)
Itin, Y.: J. Math. Phys. 46, 012501 (2005)
Kawai, T.: Phys. Rev. D 49, 2862 (1994)
Kawai, T.: Phys. Rev. D 62, 104014 (2000)
Kawai, T., Shibata, K., Tanaka, I.: Prog. Theor. Phys. 104, 505 (2000)
Komar, A.: Phys. Rev. 113, 934 (1959)
Kopczyński, W.: J. Phys. A 15, 493 (1982)
Kopczyński, W.: Ann. Phys. (N.Y.) 203, 308 (1990)
Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields. Pergamon, Oxford (1980)
Leclerc, M.: Phys. Rev. D 71, 027503 (2005)
Maluf, J.W.: J. Math. Phys. 35, 335 (1994)
Maluf, J.W., de Rocha-Neto, J.F.: Phys. Rev. D 64, 084014 (2001)
Maluf, J.W., da Rocha-Neto, J.F., Toribio, T.M.L., Castello-Branco, K.H.: Phys. Rev. D 65, 124001 (2002)
Maluf, J.W., Ulhoa, S.C., Faria, F.F., da Rocha-Neto, J.F.: Class. Quantum Gravity 23, 6245 (2006)
Maluf, J.W., Veiga, M.V.O., da Rocha-Neto, J.F.: Gen. Relativ. Gravit. 39, 227 (2007)
Mielke, E.W.: Phys. Rev. D 42, 3388 (1990)
Mielke, E.W.: Phys. Rev. D 69, 128501 (2004)
Møller, C.: Ann. Phys. 12, 118 (1961a)
Møller, C.: Mat. Fys. Medd. Dan. Vid. Selsk. 1, 10 (1961b)
Møller, C.: Nucl. Phys. 57, 330 (1964)
Møller, C.: Mat. Fys. Medd. Dan. Vid. Selsk. 39, 13 (1978)
Müller-Hoissen, F., Nitsch, J.: Phys. Rev. D 28, 718 (1983)
Müller-Hoissen, F., Nitsch, J.: Gen. Relativ. Gravit. 17, 747 (1985)
Nashed, G.G.L., Shirafuji, T.: Int. J. Mod. Phys. D 16, 65 (2007)
Nester, J.M.: Int. J. Mod. Phys. A, 1755 (1989)
Nester, J.M.: J. Math. Phys. 33, 910 (1992)
Nester, J.M., Ho, F.H., Chen, C.M.: Quasilocal center-of-mass for teleparallel gravity. In: MG10 Meeting (2004). gr-qc/0403101
Nitsch, J., Hehl, F.W.: Phys. Lett. B 90, 98 (1980)
Obukhov, Yu.N., Pereira, J.G.: Phys. Rev. D 69, 128502 (1997)
Obukhov, Yu.N., Pereira, J.G.: Phys. Rev. D 67, 044016 (2003)
Sáez, D.: Phys. Rev. D 27, 2839 (1983)
Sáez, D., Ibańez, J.M., Arnau, J.V.: Prog. Theor. Phys. 78, 800 (1987)
Stewart, B.W., Papadopoulos, D., Witten, L., Berezdivin, R., Herrera, L.: Gen. Relativ. Gravit. 14, 97 (1982)
Szabados, L.B., Quasi-local energy-momentum and angular momentum in GR: a review article, Living Rev. Relativ. 7, 4 (2007). http://www.livingreviews.org/lrr-2004-4
Tung, R.S., Nester, J.M.: Phys. Rev. D 60, 021501 (1999)
Voorhees, B.H.: Phys. Rev. D 2, 2119 (1970)
Winicour, J.: Angular momentum in general relativity. In: Held, A. (ed.) General Relativity and Gravitation. Plenum, New York (1980)
Xu, S., Jing, J.: Class. Quantum Gravity 23, 4659 (2006)
Yang, I.C., Radinschi, I.: Mod. Phys. Lett. A 17, 1159 (2002)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nashed, G.G.L. Axially symmetric solution in teleparallel equivalent of general relativity, energy, momentum and angular momentum. Astrophys Space Sci 330, 367–372 (2010). https://doi.org/10.1007/s10509-010-0389-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-010-0389-8