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Kumar, Sachin; Gupta, Y. K.

Generalized invariant solutions for spherical symmetric non-conformally flat fluid distributions of embedding class one. (English) Zbl 1307.83027

Int. J. Theor. Phys. 53, No. 6, 2041-2050 (2014).
Summary: In the present article, using the Lie group of transformations technique all the invariant solutions of Einstein’s field equations for non-conformally flat perfect fluid spheres of embedding class one have been derived by considering a 5-flat space. The same problem for conformally flat case was tackled by S. Thakadiyil and M. K. Jasim [Int. J. Theor. Phys. 52, No. 11, 3960–3964 (2013; Zbl 1282.83008)] using the same technique but with the lesser number of symmetries and hence could obtain only lesser number of solutions as compared to the number of solutions in this paper. All the solutions thus obtained have been subjected to reality conditions. As far as the authors are aware some of the solutions are new.

Cited in 4 Documents

MSC:

83C55 Macroscopic interaction of the gravitational field with matter (hydrodynamics, etc.)

Keywords:

spherical symmetric; perfect fluid spheres; embedding class one; general relativity

Citations:

Zbl 1282.83008
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Full Text: DOI

References:

[1] Anchordoqui, L. A.; Perez-Bergliaffa, S. E., No article title, Phys. Rev. D, 62 (2000) · doi:10.1103/PhysRevD.62.067502
[2] Barnes, A., No article title, Gen. Relativ. Gravit., 4, 105 (1973) · Zbl 0334.76059 · doi:10.1007/BF00762798
[3] Barnes, A., No article title, Gen. Relativ. Gravit., 5, 147 (1974) · Zbl 0346.53013 · doi:10.1007/BF00763496
[4] Bhutani, O. P.; Singh, K., No article title, J. Math. Phys., 39, 3203 (1998) · Zbl 1001.83011 · doi:10.1063/1.532248
[5] Bluman, G.W., Cole, J.D.: Similarity Methods for Differential Equations. Springer, Berlin (1974) · Zbl 0292.35001 · doi:10.1007/978-1-4612-6394-4
[6] Eddington, A.S.: The Mathematical Theory of Relativity, p. 149. Cambridge Univ. Press, Cambridge (1924) · JFM 50.0605.01
[7] Gupta, Y. K.; Gupta, R. S., No article title, Gen. Relativ. Gravit., 6, 641 (1986) · doi:10.1007/BF00769932
[8] Gupta, Y. K.; Sharma, J. R., No article title, J. Math. Phys., 37, 1962 (1996) · Zbl 0866.76101 · doi:10.1063/1.531487
[9] Gupta, Y. K.; Sharma, S. P.; Gupta, R. S., No article title, J. Math. Phys., 25, 3510 (1984) · Zbl 0556.76127 · doi:10.1063/1.526121
[10] Gupta, Y. K.; Pratibha; Kumar, S., No article title, Int. J. Mod. Phys. A, 25, 1863 (2010) · Zbl 1193.83027 · doi:10.1142/S0217751X10048263
[11] Gupta, Y. K.; Kumar, S.; Pratibha, No article title, Astrophys. Space Sci., 332, 49 (2011) · Zbl 1213.83047 · doi:10.1007/s10509-010-0582-9
[12] Kohler, H.; Chao, K. L., No article title, Z. Naturforsch. A, 20, 1537 (1965)
[13] Krishna Rao, J., No article title, Gen. Relativ. Gravit., 2, 385 (1971) · Zbl 0344.76069 · doi:10.1007/BF00758157
[14] Kumar, M.; Gupta, Y. K., No article title, Pramana J. Phys., 74, 883 (2010) · doi:10.1007/s12043-010-0081-0
[15] Kumar, S.; Gupta, Y. K.; Pratibha, No article title, Int. J. Mod. Phys. A, 25, 3993 (2010) · Zbl 1194.83049 · doi:10.1142/S0217751X10050184
[16] Kuzeev, R. R., No article title, Gravit. Teor. Otnosit., 16, 93 (1980)
[17] Pandey, S. N.; Gupta, Y. K., No article title, Univ. Roorkee Res. J., 7, 9 (1970)
[18] Pavsic, M., Tapia, V.: (2001). arXiv:gr-qc/0010045
[19] Randall, L.; Sundrum, R., No article title, Phys. Rev. Lett., 83, 3370 (1999) · Zbl 0946.81063 · doi:10.1103/PhysRevLett.83.3370
[20] Rayski, J., No article title, Lett. Nuovo Cimento, 18, 422 (1977) · doi:10.1007/BF02784924
[21] Robertson, H. P., No article title, Rev. Mod. Phys., 5, 62 (1933) · JFM 59.1516.04 · doi:10.1103/RevModPhys.5.62
[22] Saran, R.; Tiwari, R. N., No article title, Proc. Natl. Inst. Sci. India, a Phys. Sci., 31, 465 (1965)
[23] Singh, K. P.; Pandey, S. N., No article title, Proc. Natl. Inst. Sci. India, a Phys. Sci., 26, 665 (1960) · Zbl 0099.22303
[24] Stephani, H., No article title, Commun. Math. Phys., 4, 137 (1967) · Zbl 0152.45903 · doi:10.1007/BF01645757
[25] Stephani, H., No article title, Commun. Math. Phys., 9, 53 (1968) · Zbl 0157.32301 · doi:10.1007/BF01654031
[26] Stephani, H., Kramer, D., Maccallum, M., Hoenselaers, C., Herlt, E.: Exact Solutions of Einstein’s Field Equations. Cambridge Univ. Press, Cambridge (2003) · Zbl 1057.83004 · doi:10.1017/CBO9780511535185
[27] Szekers, P., No article title, Nuovo Cimento A, 43, 1062 (1966) · doi:10.1007/BF02756377
[28] Thakadiyil, S.; Jasim, M. K., No article title, Int. J. Theor. Phys., 52, 3960 (2013) · Zbl 1282.83008 · doi:10.1007/s10773-013-1708-y
[29] Treibergs, A.: In: International Workshop on Geometry. National Tsing Hua University, Hsinchu (2000)
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