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ENERGY OF SPHERICALLY SYMMETRIC SPACE–TIMES ON REGULARIZING TELEPARALLELISM

GAMAL G. L. NASHED

Centre for Theoretical Physics, The British University in Egypt, El-Sherouk City, Misr – Ismalia Desert Road, Postal No. 11837, P.O. Box 43, Egypt

Mathematics Department, Faculty of Science, Ain Shams University, Cairo, Egypt

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https://doi.org/10.1142/S0217751X10049037Cited by:13 (Source: Crossref)

Abstract

We calculate the total energy of an exact spherically symmetric solutions, i.e. Schwarzschild and Reissner–Nordström, using the gravitational energy–momentum 3-form within the tetrad formulation of general relativity. We explain how the effect of the inertial makes the total energy unphysical. Therefore, we use the covariant teleparallel approach which makes the energy always physical one. We also show that the inertial has no effect on the calculation of momentum.

Keywords:

PACS: 04.20.Cv, 04.20.Fy, 04.50.-h

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References

A. Trautman, Gravitation: An Introduction to Current Research, ed. L. Witten (John Wiley and Sons, New York, 1962) pp. 169–198. Google Scholar
L. D. Faddeev, Sov. Phys. Usp. 25, 130 (1982), DOI: 10.1070/PU1982v025n03ABEH004517. Crossref, Web of Science, ADS, Google Scholar
L. B. Szabados, Living Rev. Rel. 7, 4 (2004), http://www.livingreviews.org/lrr-2004-4. Crossref, Google Scholar
M. Blagojević , Gravitation and Gauge Symmetries ( Institute of Physics , Bristol , 2002 ) . Crossref, Google Scholar
J. M. Nester, Class. Quantum Grav. 21, S261 (2004), DOI: 10.1088/0264-9381/21/3/016. Crossref, Web of Science, Google Scholar
Yu. N. Obukhov and J. G. Pereira, Phys. Rev. D 67, 044016 (2003), DOI: 10.1103/PhysRevD.67.044016. Crossref, Web of Science, Google Scholar
V. C. de Andrade and J. G. Pereira, Phys. Rev. D 56, 4689 (1997), DOI: 10.1103/PhysRevD.56.4689. Crossref, Web of Science, ADS, Google Scholar
T. Ortín, Gravity and Strings (Cambridge University Press, 2004) p. 166. Crossref, Google Scholar
C. Møller , Tetrad fields and conservation laws in general relativity , Proc. Int. School of Physics "Enrico Fermi" , ed. C. Møller ( Academic Press , London , 1962 ) . Google Scholar
C. Møller , Conservation laws in the tetrad theory of gravitation , Proc. of the Conf. on Theory of Gravitation ( Gauthier-Villars , Paris , 1964 ) . Google Scholar
C. Pellegrini and J. Plebański, Mat. Fys. Scr. Dan. Vid. Selsk. 2(4), (1963). Google Scholar
F. W. Hehl , Proc. 6th School of Cosmology and Gravitation on Spin, Torsion, Rotation and Supergravity , eds. P. G. Bergmann and V. de Sabbata ( Plenum , New York , 1980 ) . Google Scholar
F. W. Hehlet al., Phys. Rep. 258, 1 (1995), DOI: 10.1016/0370-1573(94)00111-F. Crossref, Web of Science, ADS, Google Scholar
K. Hayashi, Phys. Lett. B 69, 441 (1977). Crossref, Web of Science, ADS, Google Scholar
K. Hayashi and T. Shirafuji, Phys. Rev. D 19, 3524 (1979), DOI: 10.1103/PhysRevD.19.3524. Crossref, Web of Science, ADS, Google Scholar
K. Hayashi and T. Shirafuji, Phys. Rev. D 24, 3312 (1981), DOI: 10.1103/PhysRevD.24.3312. Crossref, Web of Science, ADS, Google Scholar
M. Blagojević and M. Vasilić, Class. Quantum Grav. 5, 1241 (1988), DOI: 10.1088/0264-9381/5/9/009. Crossref, Web of Science, ADS, Google Scholar
T. Kawai, Phys. Rev. D 62, 104014 (2000), DOI: 10.1103/PhysRevD.62.104014. Crossref, Web of Science, Google Scholar
T. Kawai, K. Shibata and I. Tanaka, Prog. Theor. Phys. 104, 505 (2000), DOI: 10.1143/PTP.104.505. Crossref, Web of Science, ADS, Google Scholar
R. Aldrovandi et al. , Bringing together gravity and the quanta , Proc. Albert Einstein Century International Conference , arXiv:gr-qc/0603122 . Google Scholar
R. Aldrovandi, T. G. Lucas and J. G. Pereira, Gravitational energy–momentum conservation in teleparallel gravity , arXiv:0812.0034 . Google Scholar
T. G. Lucas, Y. N. Obukhov and J. G. Pereira, Phys. Rev. D 80, 064043 (2009), DOI: 10.1103/PhysRevD.80.064043. Crossref, Web of Science, Google Scholar
Y. N. Obukhov, J. G. Pereira and G. F. Rubilar, Class. Quantum Grav. 26, 215014 (2009), DOI: 10.1088/0264-9381/26/21/215014. Crossref, Web of Science, ADS, Google Scholar
Y. M. Cho, Phys. Rev. D 14, 2521 (1976), DOI: 10.1103/PhysRevD.14.2521. Crossref, Web of Science, ADS, Google Scholar
F. Gronwald, Int. J. Mod. Phys. D 6, 263 (1997), DOI: 10.1142/S0218271897000157. Link, Web of Science, ADS, Google Scholar
U. Muench, Über teleparallele gravitationstheorien, Diploma thesis, University of Cologne (1997) . Google Scholar
R. Tresguerres, Int. J. Geom. Meth. Mod. Phys. 5, 905 (2008), DOI: 10.1142/S0219887808003120. Link, Web of Science, Google Scholar
Yu. N. Obukhov and J. G. Pereira, Phys. Rev. D 69, 128502 (2004), DOI: 10.1103/PhysRevD.69.128502. Crossref, Web of Science, Google Scholar
Yu. N. Obukhov, G. F. Rubilar and J. G. Pereira, Phys. Rev. D 74, 104007 (2006), DOI: 10.1103/PhysRevD.74.104007. Crossref, Web of Science, Google Scholar
F. W. Hehlet al., Phys. Rep. 258, 1 (1995), DOI: 10.1016/0370-1573(94)00111-F. Crossref, Web of Science, ADS, Google Scholar
Yu. N. Obukhov, Int. J. Geom. Meth. Mod. Phys. 3, 95 (2006), http://www.worldscinet.com/ijgmmp/ DOI: 10.1142/S021988780600103X. Link, Web of Science, Google Scholar
J. W. Maluf, F. F. Faria and S. C. Ulhoa, Class. Quantum Grav. 24, 2743 (2007), DOI: 10.1088/0264-9381/24/10/017. Crossref, Web of Science, ADS, Google Scholar
G. G. L. Nashed, Mod. Phys. Lett. A 21, 2241 (2006), DOI: 10.1142/S0217732306020445. Link, Web of Science, ADS, Google Scholar
Y. Itin, Class. Quantum Grav. 19, 173 (2002), DOI: 10.1088/0264-9381/19/1/311. Crossref, Web of Science, ADS, Google Scholar
Y. Itin, J. Math. Phys. 46, 012501 (2005), DOI: 10.1063/1.1819523. Crossref, Web of Science, Google Scholar
F. W. Hehlet al., Phys. Lett. B 78, 102 (1978). Crossref, Web of Science, ADS, Google Scholar
F. W. Hehl, Four lectures on Poincaré gauge theory, Proc. 6th School of Cosmology and Gravitation Course on Spin, Torsion, Rotation and Supergravity, eds. P. G. Bergmann and V. De Sabbata (Plenum, New York, 1980) p. 5. Google Scholar
F. Gronwald and F. W. Hehl , On the gauge aspects of gravity , Proc. 14th Course of Int. School of Cosmology and Gravitation: Quantum Gravity , eds. P. G. Bergmann et al. ( World Scientific , Singapore , 1996 ) , arXiv:gr-qc/9602013 . Google Scholar
M. Leclerc, Phys. Rev. D 71, 027503 (2005), DOI: 10.1103/PhysRevD.71.027503. Crossref, Web of Science, Google Scholar
T. Kawai, Phys. Rev. D 49, 2862 (1994), DOI: 10.1103/PhysRevD.49.2862. Crossref, Web of Science, Google Scholar
T. Kawai, Phys. Rev. D 62, 104014 (2000), DOI: 10.1103/PhysRevD.62.104014. Crossref, Web of Science, Google Scholar
W. Kopzyński, J. Phys. A 15, 493 (1982). Crossref, ADS, Google Scholar
J. Nitsch and F. W. Hehl, Phys. Lett. B 90, 98 (1980). Crossref, Web of Science, ADS, Google Scholar
P. Baekler and F. W. Hehl, Int. J. Mod. Phys. D 15, 635 (2006), DOI: 10.1142/S0218271806008589. Link, Web of Science, ADS, Google Scholar
E. W. Mielke, Phys. Rev. D 69, 128501 (2004), DOI: 10.1103/PhysRevD.69.128501. Crossref, Web of Science, Google Scholar
G. G. L. Nashed and T. Shirafuji, Int. J. Mod. Phys. D 16, 65 (2007), DOI: 10.1142/S0218271807009310. Link, Web of Science, ADS, Google Scholar