Absolute Parallelism in The Bainchi-Type IX Taub Solution

Abstract

In this work, we study one of the famous gravitation problems in an alternative point of view

which is known as the absolute parallelism. Considering Taub solution of the Bainchi-Type IX space-time and

the Hamiltonian approach technique of absolute parallelism, we obtain corresponding angular momentum, total

energy and momentum distributions. It is seen that our main results agree with those ones published in the literature

by other author.

Keywords

• Angular momentum,energy,teleparallel gravity

Bianchi-Tipi IX Taub Çözümünde Mutlak Paralelizm

Abstract

Bu çalışmada, mutlak paralellizm olarak bilinen alternatif bir bakış açısıyla ünlü kütleçekim problemlerinden

birini inceliyoruz. Bainchi-Type IX uzay-zamanın Taub çözümü ve mutlak paralellizmde Hamilton yaklaşımı

tekniği göz önüne alındığında, bu duruma karşılık gelen açısal momentum, toplam enerji ve momentum dağılımları

elde edilmektedir. Temel sonuçlarımızın diğer bir yazar tarafından literatürde yayınlanan sonuçlarla uyumlu

olduğu görülmektedir.

Keywords

• Açısal momentum,enerji,mutlak paralelizm

References

1. Abedi H, Salti M, 2015. Multiple field modified gravity and localized energy in teleparallel framework. Gen. Relativ. Gravit., 8(47):1-14.
2. Bergmann PG, Thompson R, 1953. Spin and angular momentum in general relativity. Phys. Rev., 89: 400-407.
3. Einstein A, 1915. Preuss, Sitzungsber. Preuss. Akad. Wiss. Berlin, 47: 78.
4. Halpern P, 2006. Energy of the Taub cosmological solution. Astrophys Space Sci., 306, 279-283.
5. Hehl FW, 1980. Proceeding of the 6h School of Cosmology and Gravitation on Spin, Torsion, Rotation and Supergravity. Erice, edited by P. Bergmann and V. de Sabbata, Plenum, New york, USA.
6. Landau LD, Liftshitz EM, 1951. The Classical Theory of Fields. Addison-Wesley Press, Reading, MA.
7. Maluf JW, 1994. Hamiltonian formulation of the teleparallel description of general relativity. J. Math. Phys., 35: 335-343.
8. Maluf JW, 1995. Localization of energy in general relativity. J. Math. Phys., 36: 4242-4247.

9. Maluf JW, Martins EF, Kneip A, 1996. Gravitational energy of rotating black holes. J. Math. Phys., 37: 6302-6310.
10. Maluf JW, da Rocha-Neto JF, 1999. General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry. Gen. Rel. Grav., 31: 173-185.
11. Maluf JW, da Rocha-Neto JF, 2001. Hamiltonian formulation of general relativity in the teleparallel geometry. Phys. Rev. D, 64: 084014.
12. Maluf JW, da Rocha-Neto JF, Torbio TML, Castello-Branco KH, 2002. Energy and angular momentum of the gravitational field in the teleparallel geometry. Phys. Rev. D, 65: 124001.
13. Maluf JW, Ulhoa SC, Faria FF, da Rocha Neto JF, 2006. The angular momentum of the gravitational field and the Poincaré group. Class. Quant. Grav., 23: 6245.
14. Maluf JW, Ulhoa SC, 2009. On the gravitational angular momentum of rotating sources. Gen. Rel. and Grav., 41(6): 1233-1247.
15. Maluf JW, 2013. The teleparallel equivalent of general relativity. Annalen der Physik, 525(5): 339-357.
16. Møller C., 1958. On the localization of the energy of a physical system in the general theory of relativity. Ann. Phys. (N.Y.), 4: 347-371.
17. Nashed GGL, 2008. Charged dilaton, energy, momentum and angular-momentum in teleparallel theory equivalent to general relativity. Eur. Phys. J. C, 54: 291-302.
18. Nashed GGL, 2010. Brane world black holes in teleparallel theory equivalent to general relativity and their Killing vectors, energy, momentum and angular momentum. Chin. Phys. B, 19: 020401.
19. Papapetrou A, 1948. Einstein's theory of gravitation and flat space. Proc. R. Ir. Acad., 52: 11-23.
20. Qadir A, Sharif M, 1992. General formula for the momentum imparted to test particles in arbitrary spacetimes. Phys. Lett. A, 167: 331- 334.
21. Rocha-Neto JF, Maluf JW, 2014. The angular momentum of plane-fronted gravitational waves in the teleparallel equivalent of general relativity. Gen. Rel. Grav., 46: 1667.
22. Salti M, Acikgoz I, 2013. Black holes, wormholes and the Hamiltonian approach in the framework of teleparallel gravity. Physica Scripta 87(4): 045006.
23. Sharif M, Taj S, 2010. Energy Contents of Gravitational Waves in Teleparallel Gravity. Mod. Phys. Lett. A, 25: 221-232.
24. Sousa AA, Pareira RB, 2006. Angular momentum of the BTZ black hole in the teleparallel geometry. Prog. Theor. Phys., 114: 1179-1190 .
25. Sousa AA, Moura JS, Pereira RB, 2010. Energy in an expanding universe in the teleparallel geometry. Braz. J. Phys., 40: 1-8.
26. Taub AH, 1951. Empty space-times admitting a three parameter group of motions. Ann. Math., 53: 472-490.
27. Tolman RC, 1934. Relativity, Thermodynamics and Cosmology. Oxford University Press, London, UK, 227 p.
28. Ulhoa SC, Rocha PMM, 2013. Neutron Stars in Teleparallel Gravity. Braz. J. Phys., 43(3): 162-171.
29. Weinberg S, 1972. Gravitation and Cosmlogy: Principles and Applications of General Theory of Relativity. Wiley, New York, USA, 165 p.
30. Weitzenböck R, 1923. Invarianten Theorie. Nordhoff, Groningen.