Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism

doi:10.1088/1674-1056/21/1/010401

摘要/Abstract

摘要： In the context of the covariant teleparallel framework, we use the 2-form translational momentum to compute the total energy of two general spherically symmetric frames. The first one is characterized by an arbitrary function H(r), which preserves the spherical symmetry and reproduces all the previous solutions, while the other one is characterized by a parameter ξ which ensures the vanishing of the axial of trace of the torsion. We calculate the total energy by using two procedures, i.e., when the Weitzenböck connection Γ_α^β is trivial, and show how H(r) and ξ play the role of an inertia that leads the total energy to be unphysical. Therefore, we take into account Γ_α^β and show that although the space×we use contain an arbitrary function and one parameter, they have no effect on the form of the total energy and momentum as it should be.

关键词: gravitation, teleparallel gravity, energy-momentum, conserved currents

Abstract: In the context of the covariant teleparallel framework, we use the 2-form translational momentum to compute the total energy of two general spherically symmetric frames. The first one is characterized by an arbitrary function $H(r)$, which preserves the spherical symmetry and reproduces all the previous solutions, while the other one is characterized by a parameter $\xi$ which ensures the vanishing of the axial of trace of the torsion. We calculate the total energy by using two procedures, i.e., when the Weitzenböck connection ${\varGamma_\alpha}^\beta$ is trivial, and show how $H(r)$ and $\xi$ play the role of an inertia that leads the total energy to be unphysical. Therefore, we take into account ${\varGamma_\alpha}^\beta$ and show that although the spacetimes we use contain an arbitrary function and one parameter, they have no effect on the form of the total energy and momentum as it should be.

Key words: gravitation, teleparallel gravity, energy-momentum, conserved currents

中图分类号: (Classical general relativity)

04.20.-q

04.20.Cv (Fundamental problems and general formalism) 04.20.Jb (Exact solutions) 04.50.Kd (Modified theories of gravity)

Gamal G. L. Nashed. Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism[J]. 中国物理B, 2012, 21(1): 10401-010401.

Gamal G.L. Nashed . Energy and momentum of general spherically symmetric frames on the regularizing teleparallelism[J]. Chin. Phys. B, 2012, 21(1): 10401-010401.

参考文献 49

[1]	Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (New York: Freeman)
[2]	de Andrade V C and Pereira J G 1997 Phys. Rev. D 56 4689
[3]	Trautman A 1962 it Gravitation: An Introduction to Current Research (Witten L, ed.) (New York: John Wiley and Sons) pp. 169-198
[4]	Faddeev L D 1982 it Sov. Phys. Usp. 25 130
[5]	Szabados L B 2004 it Living Rev. Rel. 7 4
[6]	Blagojević M 2002 Gravitation and Gauge Symmetries (Bristol: Institute of Physics)
[7]	Neser J M 2004 Class. Quantum Grav. 21 S261
[8]	Hehl F W, Kerlick G D and von der Heyde P 1976 Phys. Lett. 63B 446
[9]	Hehl F W, Lord E A and Smalley L L 1981 Gen. Relat. Grav. 13 1037
[10]	Hehl F W and McCrea J D 1986 Found. Phys. 16 267
[11]	Hehl F W, McCrea J D, Mielke E W and Neeman Y 1995 Phys. Reports 258 1
[12]	Hehl F W and Socorro J 1998 Acta Phys. Polon. B29 1113
[13]	Ortín T 2004 Gravity and Strings (Cambridge: Cambridge University Press) p. 166
[14]	Mo ller C 1962 Proceedings of the International School of Physics Enrico Fermi (edited by Mller C) (London: Academic Press)
[15]	Mo ller C 1964 Proceedings of the Conference on Theory of Gravitation (Gauthier-Villars, Paris, and PWN-Polish Scientific Publishers, Warszawa) (NORDITA Publications No. 136)
[16]	Pellegrini C and Pleba'nski J 1963 Mat. Fys. Scr. Dan. Vid. Selsk. 2 no.4
[17]	Hehl F W 1979 Proceedings of the 6th School of Cosmology and Gravitation on Spin, Torsion, Rotation and Supergravity Erice (New York: Plenum)
[18]	Hayashi K 1977 Phys. Lett. 69B 441
[19]	Hayashi K and Shirafuji T 1979 Phys. Rev. D 19 3524
[20]	Hayashi K and Shirafuji T 1981 Phys. Rev. D 24 3312
[21]	Blagojević Z M and Vasilić M 1988 Class. Quant. Grav. 5 1241
[22]	Kawai T 2000 Phys. Rev. D 62 104014
[23]	Kawai T, Shibata K and Tanaka I 2000 Prog. Theor. Phys. 104 505
[24]	Aldrovandi R, Guillen L C T, Pereira J G and Vu K H 2005 Proceedings of the Albert Einstein Century International Conference, Paris July 18-22
[25]	Aldrovandi R, Lucas T G and Pereira J G 2008 arXiv:0812.0034 [gr-qc]
[26]	Lucas T G, Obukhov Y N and Pereira J G 2009 Phys. Rev. D 80 064043
[27]	Obukhov Y N, Pereira J G and Rubilar G F 2009 Class. Quant. Grav. 26 215014
[28]	Nashed G G L 2002 Gen. Rel. Grav. 34 1047
[29]	Nashed G G L 2006 Mod. Phys. Lett. A 21 2241
[30]	Cho Y M 1976 Phys. Rev. D 14 2521
[31]	Gronwald F 1997 Int. J. Mod. Phys. D 6 263
[32]	Muench U 1997 über Teleparallele Gravitationstheorien Diploma Thesis (University of Cologne)
[33]	de Andrade V C and Pereira J G 1997 Phys. Rev. D 56 4689
[34]	Tresguerres R 2008 Int. J. Geom. Meth. Mod. Phys. 5 905
[35]	Obukhov Y N and Pereira J G 2003 Phys. Rev. D 67 044016
[36]	Obukhov Y N and Pereira J G 2004 Phys. Rev. D 69 128502
[37]	Obukhov Y N, Rubilar G F and Pereira J G 2006 Phys. Rev. D 74 104007
[38]	Puetzfeld D 2001 Exact Solutions and Scalar Field in Gravity: Recent Developments (Dordrecht: Kluwer) pp. 141-151
[39]	García A, Macías A, Puetzfeld D and Socorro J 2000 Phys. Rev. D 62 044021
[40]	King A D and Vassiliev D 2001 Class. Quantum Grav. 18 2317
[41]	Pasic V and Vassiliev D 2005 Class. Quantum Grav. 22 3961
[42]	Vassiliev D 2002 Gen. Rel. Grav. 34 1239
[43]	Vassiliev D 2005 Ann. Phys. (Leipzig) 14 231
[44]	Obukhov Y N 2006 Phys. Rev. D 73 024025
[45]	Obukhov Y N 2006 Int. J. Geom. Meth. Mod. Phys. 3 95
[46]	Shirafuji T, Nashed G G L and Hayashi K 1996 Prog. Theor. Phys. 95 665
[47]	Robertson H P 1932 Ann. Math. (Princeton) 33 496
[48]	Nashed G G L and Shirafuji T 2007 Int. J. Mod. Phys. D 16 65
[49]	Nashed G G L 2010 Int. J. Mod. Phys. A 25 2883