Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum

doi:10.1088/1674-1056/19/2/020401

摘要/Abstract

摘要： The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time their energies are different. Therefore, a regularized expression of the gravitational energy--momentum tensor of the teleparallel equivalent of general relativity (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy--momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space--times are calculated. In spite of using a static space--time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space--times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.

Abstract: The energy--momentum tensor, which is coordinate-independent, is used to calculate energy, momentum and angular momentum of two different tetrad fields. Although, the two tetrad fields reproduce the same space--time their energies are different. Therefore, a regularized expression of the gravitational energy--momentum tensor of the teleparallel equivalent of general relativity (TEGR), is used to make the energies of the two tetrad fields equal. The definition of the gravitational energy--momentum is used to investigate the energy within the external event horizon. The components of angular momentum associated with these space--times are calculated. In spite of using a static space--time, we get a non-zero component of angular momentum! Therefore, we derive the Killing vectors associated with these space--times using the definition of the Lie derivative of a second rank tensor in the framework of the TEGR to make the picture more clear.

Key words: teleparallel equivalent of general relativity, brane world black holes, gravitational energy--momentum tensor, regularized expression of the gravitational energy--momentum

中图分类号: (Physics of black holes)

04.70.-s

04.50.-h (Higher-dimensional gravity and other theories of gravity) 11.25.Wx (String and brane phenomenology) 04.20.Gz (Spacetime topology, causal structure, spinor structure) 02.40.-k (Geometry, differential geometry, and topology)

Gamal G.L. Nashed. Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum[J]. 中国物理B, 2010, 19(2): 20401-020401.

Gamal G.L. Nashed. Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum[J]. Chin. Phys. B, 2010, 19(2): 20401-020401.

参考文献 69

[1]	Kaluza T 1920 Sitzungseber. Press. Akad. Wiss.Phys. Math. KlasseK1 966
[1a]	Klein O 1926 Z. Phys. 37 895
[2]	Ho?ava P and Witten E 1996 Nucl.Phys. B 460 506
[2a]	Ho?ava P and Witten E 1996 Nucl. Phys. B 4 7594
[3]	Randall L and Sundrum R 1999 Phys. Rev. Lett. 8 3 3370 4690
[4]	Shiromizu T, Maeda K and Sasaki M 2000 Phys. Rev. D 62 024012
[5]	Bronnikov K A, Melnikov V N and Dehnen H 2003 Phys. Rev. D 68 024025
[6]	Bronnikov K A, Clément G,Constantinidis C P and Favris J C 1998 Phys. Lett. A 24 3 121
[6a]	Bronnikov K A, Clément G, Constantinidis C P andFavris J C 1998 Grav. Cos. 4 128
[7]	Kibble T W B 1961 J. Math. Phys. 2 212
[8]	Hehl F W, von der Heyde P, Kerlick D andNester J 1976 Rev. Mod. Phys. 48 393
[9]	Hehl F W 1980 General Relativity and Gravitation: One Hundred Yearsafter the Birth of Albert Einstein ed. Held A (New York: Plenum)Vol. 1
[10]	Hayashi K and Shirafuji T 1980 Prog. Theor. Phys. 64 866, 883, 1435, 2222
[10a]	Hayashi K and Shirafuji T 1980 Prog.Theor. Phys. 65 525
[11]	Blagojevi? M and Nikoli? I A 2000 Phys. Rev. D 62 024021
[12]	Hehl F W, Nitsch J and von der Heyde P1980 General Relativity and Gravitation Held A ed. (New York: Plenum)
[13]	Hehl F W, MacCrea J D, Mielke E W and Neèman Y 1995 Phys. Rep. 258 1
[14]	Hayashi K and Shirafuji T 1979 Phys. Rev. D 19 3524
[15]	Nitsch J 1980 Cosmology and Gravitation: Spin,Torsion, Rotation and Supergravity eds. Bergman P G and deSabbata V (New York: Plenum)
[16]	Bergmann P G and Thomson R 1953 Phys. Rev. 89 401
[17]	Landau L D and Lifshitz E M 1980 The Classical Theory ofFields (Oxfor: Pergamon Press)
[18]	Pellegrini C and Plebanski J 1963 Mat. Fys. Scr. Dan. Vid. Selsk. 2 No.3
[19]	M?ller C 1961 Ann. Phys. 12 118
[20]	M?ller C 1962 ``Tetrad Fields and Conservation Laws inGeneral Relativity'' in Proc. International School of Physics``Enrico Fermi"} ed. M?ller C (London: Academic Press)
[21]	M?ller C 1961 Mat. Fys. Medd. Dan. Vid. Selsk. 1 10
[22]	M?ller C 1964 Nucl. Phys. 57 330
[23]	Hayashi K and Nakano T 1967 Prog. Theor. Phys. 38 491
[24]	Kopzyński W 1982 J. Phys. A 15 493
[25]	Chang C C, Nester J M and Chen C M 1999 Phys. Rev. Lett. 8 3 1897
[25a]	Tung R S and Nester J M 1999 Phys. Rev. D 60 021501
[25b]	Nester J M and Yo Chin H J 1999 J. Phys. 37 113
[25c]	Nester J M, Ho F H and Chen C M 2003 Quasilocal Center-of-Mass for Teleparallel Gravity, Proceeding ofthe 10th. Marcel Grossman Meeting (Rio de Janeiro)} gr-qc/0403101
[25d]	Nester J M 1989 Phys. Lett. A 139 112
[25e]	Nester J M 1992 J. Math. Phys. 3 3 910
[25f]	Nester J M 1988 Class.Quantum Grav. 5 1003
[26]	Toma N 1991 Prog. Theor. Phys. 86 659
[26a]	Kawai T and Toma N 1992 Prog. Theor. Phys. 87 583
[27]	de Andrade V C and Pereira J G 1997 Phys. Rev. D 56 4689
[27a]	de Andrade V C, Guillen L C T and Pereira J G 2000 Phys.Rev. Lett. 84 4533
[27b]	de Andrade V C, Guillen L C T and Pereira J G2001 Phys. Rev. D 64 027502
[28]	Maluf J W and da Rocha-Neto J F 2001 Phys. Rev. D 64 084014
[29]	Schwinger J 1963 Phys. Rev. 130 1253
[30]	Maluf J W 1994 J. Math. Phys. 35 335
[30a]	Maluf J W and Kneip A 1997 J. Math. Phys. 38 458
[30b]	MalufJ W and da Rocha-Neto J F 1999 J. Math. Phys. 40 1490
[30c]	Maluf J W and Goya A 2001 Class. Quantum Grav. 18 5143
[30d]	Maluf J W, da Rocha-Neto J F, Toribio T M L and Castello-Branco K H2002 Phys. Rev. D 65 124001
[30e]	Sousa A A and Maluf J W2002 Prog. Theor. Phys. 108 457
[31]	da Rocha-Neto J F andCastello-Branco K H 2003 JHEP 0311 002
[32]	Regge T and Teitelboim C 1974 Ann. Phys.(NewYork) 88 286
[33]	York Jr. J W 1980 Energy and Momentum of theGravitational Field, in ``Essays in General Relativity'' ed.Tipler F J (New York: Acdemic Press)
[34]	Beig R and Murchadha N ó 1987 Ann.Phys.(New York) 174 463
[35]	Szabados L B 2003 Class. Quantum Grav. 20 2627
[36]	Maluf J W and Sousa A A 2000 Hamiltonian Formulation of TeleparallelTheories of Gravity in the Time Gauge gr-qc/0002060
[37]	Sousa A A and Maluf J W 2000 Prog. Theor. Phys. 104 531
[38]	Maluf J W and de Rocha-Neto J F 2001 Phys. Rev. D 64 084014
[39]	Maluf J W, Ulhoa S C, Faria F F and da Rocha-Neto J F2006 Calss. Quantum Grav. 23 6245
[40]	Sousa A A, Pereira R B and da Rocha-Neto J F 2005 Prog. Theor. Phys. 1141179
[40a]	Sousa A A, Moura J S and Pereira R B gr-qc/0702109
[41]	Xu S X and Jing J L 2006 Class. Quantum Grav. 23 4659
[42]	Nester J M 1989 Int. J. Mod. Phys. A 4 1755
[43]	Blagojevi? M and Vasili? M 2001 Phys. Rev.D 64 044010
[44]	Change C C and Nester J M 2000 Grav. & Cosmol. 6 257
[45]	So L L, Nester J M and Chen H 2006 The 7th.Conference on Gravitation and Astrophysics gr-qc/0605150
[46]	Szabados L B 2004 ``Quasi-Local Energy--Momentum and Angular Momentum in GR: A Review Article'',Living Rev. Relativity 7 4,http://www.livingreviews.org/lrr-2004-4.
[47]	Maluf J W 2005 Annalen Phys. 14723
[47a]	Maluf J W Gravitational and Cosmology 11 284
[48]	Christodoulou D 1970 Phys. Rev. Lett. 25 1596
[49]	Bergqvist G 1992 Class. Quantum Grav. 9 1753
[50]	Komar A 1959 Phys. Rev. 11 3 934
[50a]	Winicour J 1980 ``Angular Momentum in General Relativity'', inGeneral Relativity and Gravitation } ed. Held A (New York: Plenum)
[50b]	Ashtekar A ``Angular Momentum of Isolated Systems in GeneralRelativity'', in Cosmology and Gravitation ed. Bergmann P G andde Sabbata V 1980 (New York: Plenum)
[51]	Hayashi K and Shirafuji T 1985 Prog. Theor.Phys. 7 3 54
[51a]	Blagojevi? M and Vasili?M 1988 Class. Quantum Grav. 5 1241
[51b]	Kawai T 2000 Phys. Rev. D 62 104014
[51c]	Kawai T, Shibata K and Tanaka I 2000 Prog. Theor. Phys. 104 505
[52]	Dirac P A M 1964 Lectures on Quantum Mechanics (Belfer Gradute Schoolof Science (Monographs Series No. 2) (New York: YeshivaUniversity)
[53]	Robertson H P 1932 Ann. Math.(Princeton) 3 3 496
[54]	Hayashi K and Shirafuji T 1979 Phys. Rev. D 19 3524
[55]	Shirafuji T, Nashed G G L and Hayashi K 1996 Prog. Theor. Phys. 95 665
[56]	Salti M and Aydo?du Oand Korunur M appear in JHEP} gr-qc/0611014
[57]	Arnowitt R, Deser S and Misner C W 1962 Gravitation: An Introduction to Current Research } ed. Witten L (NewYouk: Wiley)
[58]	Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (San Francisco: Freeman) p435
[59]	Casadio R, Fabbri A and Mazzacurati L 2002 Phys. Rev. D 65 084040
[60]	Germani C and Maartens R 2001 Phys. Rev. D 64 124010
[61]	Bronnikov K A and Kim S W 2003 Phys. Rev. D 67 064027
[62]	Maluf J W, Veiga M V O and da Rocha-Neto J F 2007 Gen. Rel. Grav. 39 227
[63]	Bae(c)kler P, Hecht R, Hehl F W and Shirafuji T 1987 Prog. Theor. Phys. 78 16
[64]	Brown J D and York J W Jr. 1991 Quasi-Local Energy in General Relativity, Proceedings of the Joint SummerResearch Conference on Mathematical Aspects of Classical FieldTheory, ed. Gotay M J, Marsden J E and Moncrief V (AmericanMathematical Socity)
[64a]	Brown J D and York J W Jr. 1993 Phys. Rev. D 47 1407
[65]	Sharif M and Jamil Amir M 2008 Mod. Phys. Lett. A 23 969
[66]	Kramer D, Stephani H, MacCullum M A H andHerlt E 1980 Exact Solutions of Einstein Field Equations(Cambridge: Cambridge University Press)
[67]	Hall G S 2004 Symmetryies and Curvature Structure inGeneral Relativity (Sigapore: World Scientific)
[68]	Feroze T, Mahomed F M and Qadir A 2006 NonlinearDynam. 45 65
[69]	M?ller C 1966 Mat. Fys. Medd. Dan. Vid. Selsk. 35 No. 3.