Moller Energy--Momentum Complex in General Relativity for Higher Dimensional Universes
M. Aygun1, S. Aygun1, .I.Yilmaz1, H. Baysal2, .I. Tarhan1
1Department of Physics, Art and Science Faculty, Canakkale Onsekiz Mart University, 17020 Canakkale, Turkey2Department of Secondary Science and Mathematics Education, Facultyof Education,Canakkale Onsekiz Mart University, 17100 Canakkale, Turkey
Moller Energy--Momentum Complex in General Relativity for Higher Dimensional Universes
M. Aygun1;S. Aygun1;.I.Yilmaz1;H. Baysal2;.I. Tarhan1
1Department of Physics, Art and Science Faculty, Canakkale Onsekiz Mart University, 17020 Canakkale, Turkey2Department of Secondary Science and Mathematics Education, Facultyof Education,Canakkale Onsekiz Mart University, 17100 Canakkale, Turkey
摘要Using the Moller energy--momentum definition in general relativity (GR) we calculate the total energy--momentum distribution associated with (n+2)-dimensional homogeneous and isotropic model of the universe. It is found that total energy of Moller is vanishing in (n+2) dimensions everywhere but n-momentum components of Moller in (n+2) dimensions are different from zero. Also, we evaluate the static Einstein Universe, FRW universe and de Sitter universe in four dimensions by using (n+2)-type metric, then calculate the Moller energy--momentum distribution of these spacetimes. However, our results are consistent with the results of Banerjee and Sen, Xulu, Radinschi, Vargas, Cooperstock-Israelit, Aygun et al., Rosen, and Johri et al. in four dimensions.
Abstract:Using the Moller energy--momentum definition in general relativity (GR) we calculate the total energy--momentum distribution associated with (n+2)-dimensional homogeneous and isotropic model of the universe. It is found that total energy of Moller is vanishing in (n+2) dimensions everywhere but n-momentum components of Moller in (n+2) dimensions are different from zero. Also, we evaluate the static Einstein Universe, FRW universe and de Sitter universe in four dimensions by using (n+2)-type metric, then calculate the Moller energy--momentum distribution of these spacetimes. However, our results are consistent with the results of Banerjee and Sen, Xulu, Radinschi, Vargas, Cooperstock-Israelit, Aygun et al., Rosen, and Johri et al. in four dimensions.
M. Aygun;S. Aygun;.I.Yilmaz;H. Baysal;.I. Tarhan. Moller Energy--Momentum Complex in General Relativity for Higher Dimensional Universes[J]. 中国物理快报, 2007, 24(7): 1821-1824.
M. Aygun, S. Aygun, .I.Yilmaz, H. Baysal, .I. Tarhan. Moller Energy--Momentum Complex in General Relativity for Higher Dimensional Universes. Chin. Phys. Lett., 2007, 24(7): 1821-1824.
[1] Einstein A 1915 Preuss. Akad. Wiss. Berlin 47 778 [2] Tolman R C 1934 Relativity, Thermodynamics andCosmology (Oxford: Oxford University Press) p 227 [3] Papapetrou A 1948 Proc. R. Ir. Acad. A 52 11 [4] Landau L D and Lifshitz E M 1951 The Classical Theory ofFields (Reading, MA: Addison-Wesley) [5] Bergmann P G and Thomson R 1953 Phys. Rev. 89 400 [6] Goldberg J N 1959 Phys. Rev. 111 315 [7] Weinberg S 1972 Gravitation and Cosmology: Principlesand Applications of General Theory of Relativity (New York: Wiley) [8] M{\oller C 1958 Ann. Phys. $($N. Y.$)$ 4 347 [9] Xulu S S 2000 Mod. Phys. Lett. A 15 1511 Xulu S S PhD Thesis hep-th/0308070 Xulu S S 2003 Astrophys. Space. Sci. 283 23 Vagenas E C 2004 Mod. Phys. Lett. A 19 213 Gad R 2005 Astrophys. Space Sci. 295 459 [10] Radinschi I 2000 Fizika B 9 203 Radinschi I 2000 Mod. Phys. Lett. A 15 2171 Radinschi I 2001 Chin. J. Phys. 39 231 Radinschi I 2001 Mod. Phys. Lett. A 16 673 [11] Lessner G 1996 Gen. Rel. Grav. 28 527 [12] Virbhadra K S 1999 Phys. Rev. D 60 104041 [13] Virbhadra K S 1990 Phys. Rev. D 41 1086 Virbhadra K S 1990 Phys. Rev. D 42 2919 Rosen N and Virbhadra K S 1993 Gen. Rel. Grav. 25 429 Virbhadra K S 1995 Pramana J. Phys. 45 215 Vagenas E C 2003 Int. J. Mod. Phys. A 18 5949 Sharif M 2004 Nuovo Cimento B 19 463 Sharif M 2004 Int. J. Mod. Phys. D 13 1019 Gad R 2004 Mod. Phys. Lett. A 19 1847 [14] Rosen N 1995 Gen. Rel. Grav. 26 323 [15] Johri J B, Kalligas D, Singh G P and Everitt C W F 1995 Gen. Rel. Grav. 27 323 [16] Banerjee N and Sen S 1997 Pramana J. Phys. 49 609 [17] Albrow M G 1973 Nature 241 56 [18] Tryon E P 1973 Nature 246 396 [19] Cooperstock F I 1994 Gen. Rel. Gravit. 26 323 Cooperstock F I and Israelit M 1995 Fond. Phys. 25 631 [20] Aydogdu O 2006 Int. J. Mod. Phys. A 21 3845 Aydogdu O 2006 Int. J. Mod. Phys. D 15 459 Aydogdu O 2006 Fortschritte der Physik 54 246 Salt{\i M and Havare A 2005 Int. J. Mod. Phys. A 20 2169 Salt{\i M 2005 Astrophys. Space Sci. 299 159 Aydogdu O, Salt{\i M and Korunur M 2005 Acta Phys. Slov. 55 537 [21] Vargas T 2004 Gen. Rel. Gravit. 36 1255 [22] Ayg\"{un S, Ayg\"{un M and Tarhan \.I 2007 Pramana J.Phys. 68 21 [23] Ayg\"{un S, Baysal H and Tarhan \.I 2007 in press: Int. J. Theor. Phys. DOI:10.1007/s10773-007-9375-5 [24] Vagenas E C 2003 Int. J. Mod. Phys A 18 5949 Vagenas E C 2003 Int. J. Mod. Phys. A 18 5781 Vagenas E C 2005 Int. J. Mod. Phys. D 14 573 Grammenos Th 2005 Mod. Phys. Lett. A 20 1741 Radinschi I and Grammenos Th 2006 Int. J. Mod. Phys. A 21 2853 [25] Lessner G 1996 Gen. Rel. Grav. 28 527 [26] Chodos A and Detweiler S 1980 Phys. Rev. D 21 2167 [27] Marciano W J 1984 Phys. Rev. Lett. 52 489 [28] Sahdev D 1984 Phys. Rev. D30 2495 [29] Emelyanov V M, Nikitin Yu P, Rozental J L and Berkov A V 1986 Phys. Rep. 143 1 [30] Chatterjee S and Bhui B 1993 Int. J. Theor. Phys. 32 671 [31] Overduin J M and Wesson P S 1987 Phys. Rep. 283 303 [32] Misner C W, Thorne K S and Wheeler J A 1973 Gravitation (New York: Freeman) [33] Cooperstock F I and Sarracino R S 1978 J. Phys. A: Math. Gen. 11 877 [34] Ayg\"{un S, Tarhan \.I and Baysal H 2007 Chin. Phys.Lett. 24 355 [35] Ayg\"{un S 2007 Acta Phys. Pol. B 38 73