Cosmic String in Bianchi Type-III Space-Time with Bulk Viscosity and Magnetic Field

Author(s)
Sharad Panditrao Kandalkar^{*},
Amrapali Pandurang Wasnik,
Sunita Padmakar Gawande,
Mohini Nilkanth Gaikwad

Affiliation(s)

Department of Mathematics, Government Vidarbha Institute of Science and Humanities, Amravati, India.

Department of Mathematics, Government Vidarbha Institute of Science and Humanities, Amravati, India.

ABSTRACT

We investigate some locally rotationally symmetric (LRS) Bianchi type-III string cosmological model in the presence of bulk viscosity and magnetic field, where an equation of state and relation between metric potential are considered. The solution describes a shearing and non-rotating model with big-bang start. In the absence of magnetic field it reduces to a string model with bulk viscosity, where the relation between the coefficient of bulk viscosity and the energy density is for a = 0.

We investigate some locally rotationally symmetric (LRS) Bianchi type-III string cosmological model in the presence of bulk viscosity and magnetic field, where an equation of state and relation between metric potential are considered. The solution describes a shearing and non-rotating model with big-bang start. In the absence of magnetic field it reduces to a string model with bulk viscosity, where the relation between the coefficient of bulk viscosity and the energy density is for a = 0.

Cite this paper

S. Kandalkar, A. Wasnik, S. Gawande and M. Gaikwad, "Cosmic String in Bianchi Type-III Space-Time with Bulk Viscosity and Magnetic Field,"*International Journal of Astronomy and Astrophysics*, Vol. 2 No. 4, 2012, pp. 225-229. doi: 10.4236/ijaa.2012.24029.

S. Kandalkar, A. Wasnik, S. Gawande and M. Gaikwad, "Cosmic String in Bianchi Type-III Space-Time with Bulk Viscosity and Magnetic Field,"

References

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[11] T. Singh and A. Beeshan, “Bulk Viscous Cosmological Models with variable G and Lambda,” General Relativity Gravitation, Vol. 30, 1998, pp. 573-578.

[12] R. Bali and S. Dave, “Bianchi Type-III String Cosmological Models with Bulk Viscous Fluid in General Relativity,” Astrophysics and Space Science, Vol. 282, No. 1, 2002, pp. 461-467.

[13] M. A. Melvin, “Homogeneous Axial Cosmologies with Electromagnetic Fields and Dust,” Annals of the New York Academy of Sciences, Vol. 262, No. 2, 1975, pp. 253-274.

[14] A. Banerjee, A. Sanyal and S.Chakraborty, “String Cosmology in Bianchi I Space-Time,” Pramana, Journal of Physics, Vol. 34, No. 1, 1990, pp. 1-11.

[15] G. P. Singh and J. Singh, “String Cosmological Models with Magnetic Field,” General Relativity Gravitation, Vol. 31, No. 3, 1999, pp. 371-378. doi:10.1023/A:1026644828215

[16] R. Bali and R. D. Upadhaya, “L.R.S. Bianchi Type I String Dust Magnetized Cosmological Models,” Astrophysics and Space Science, Vol. 283, No. 1, 2003, pp. 97-108.

[17] S. K. Tripathy, S. K. Sahu and T. R. Routray, “String Cloud Cosmologies for Bianchi Type-III with Electromagnetic Field,” Astrophysics and Space Science, Vol. 315, No. 1-4, 2008, pp. 105-110.

[18] M. K. Yadav, A. Pradhan and S. K. Singh, “Some Magnetized Bulk Viscous String Cosmological Models in General Relativity,” Astrophysics and Space Science, Vol. 311, No. 4, 2007, pp. 423-429.

[19] R. Bali, R. Banerjee and S. K. Banerjee, “Bianchi Type VIo Magnetized Bulk Viscous Massive String Cosmological Model in General Relativity,” Astrophysics and Space Science, Vol. 317, No. 2, 2008, pp. 21-26.

[20] T. Takabayasi, “Theory of One-Dimensional Relativistic Elastic Continuum for the Model of Particles and Resonances,” Mathematical Physics and Applied Mathematics, Vol. 1, No. 1, 1976, pp. 179-216.

[21] R. Bali and K. Sharma, “Bianchi Type I Bulk Viscous Stiff Fluid Tilted Cosmological Model in General Relativity,” Astrophysics and Space Science, Vol. 275, No. 4, 2001, pp. 485-497.

[1] T. W. B. Kibble, “Topology of Cosmic Domains and Strings,” Journal of Physics, Vol. 9, No. 8, 1976, pp. 1387-1398.

[2] A. Vilenkin, “Cosmic Strings and Other Topological Defects,” Physical Review, Vol. 121, 1985, pp. 263-296.

[3] Ya. B. Zel’dovich, “Cosmological Fluctuations Produced Near a Singularity,” Monthly Notices of the Royal Astronomical Society, Vol. 192, 1980, pp. 663-668.

[4] P. S. Letelier, “String Cosmologies,” Physical Review D, Vol. 28, 1983, pp. 2414-2419.

[5] J. Stachel, “Thickening the String. I. The String Perfect Dust,” Physical Review D, Vol. 21, 1980, pp. 2171-2181.

[6] K. D. Krori, T. Chaudhary, C. R. Mahanta and A. Muzumdar, “Some Exact Solution in String Cosmology,” General Relativity Gravitation, Vol. 22, No. 2, 1990, pp. 123-130.

[7] X. X. Wang, “Exact Solutions for String Cosmology,” Chinese Physics Letters, Vol. 20, No. 5, 2003, pp. 615-617. doi:10.1088/0256-307X/20/5/307

[8] R. Tikekar and L. K. Patel, “Some Exact Solutions of String Cosmology in Bianchi III Space-Time,” General Relativity Gravitation, Vol. 24, No. 4, 1992, pp. 397-404.

[9] S. Chakraborty and A. K. Chakraborty, “String Cosmology in Spherically Symmetric Space Time,” Journal of Mathematical Physics, Vol. 33, No. 3, 1992, pp. 2336-2338.

[10] K. D. Krori and A. Mukherjee, “Bianchi Cosmologies with Particle Creation and Bulk Viscosity,” General Relativity Gravitation, Vol. 32, No. 8, 2000, pp. 1429- 1438.

[11] T. Singh and A. Beeshan, “Bulk Viscous Cosmological Models with variable G and Lambda,” General Relativity Gravitation, Vol. 30, 1998, pp. 573-578.

[12] R. Bali and S. Dave, “Bianchi Type-III String Cosmological Models with Bulk Viscous Fluid in General Relativity,” Astrophysics and Space Science, Vol. 282, No. 1, 2002, pp. 461-467.

[13] M. A. Melvin, “Homogeneous Axial Cosmologies with Electromagnetic Fields and Dust,” Annals of the New York Academy of Sciences, Vol. 262, No. 2, 1975, pp. 253-274.

[14] A. Banerjee, A. Sanyal and S.Chakraborty, “String Cosmology in Bianchi I Space-Time,” Pramana, Journal of Physics, Vol. 34, No. 1, 1990, pp. 1-11.

[15] G. P. Singh and J. Singh, “String Cosmological Models with Magnetic Field,” General Relativity Gravitation, Vol. 31, No. 3, 1999, pp. 371-378. doi:10.1023/A:1026644828215

[16] R. Bali and R. D. Upadhaya, “L.R.S. Bianchi Type I String Dust Magnetized Cosmological Models,” Astrophysics and Space Science, Vol. 283, No. 1, 2003, pp. 97-108.

[17] S. K. Tripathy, S. K. Sahu and T. R. Routray, “String Cloud Cosmologies for Bianchi Type-III with Electromagnetic Field,” Astrophysics and Space Science, Vol. 315, No. 1-4, 2008, pp. 105-110.

[18] M. K. Yadav, A. Pradhan and S. K. Singh, “Some Magnetized Bulk Viscous String Cosmological Models in General Relativity,” Astrophysics and Space Science, Vol. 311, No. 4, 2007, pp. 423-429.

[19] R. Bali, R. Banerjee and S. K. Banerjee, “Bianchi Type VIo Magnetized Bulk Viscous Massive String Cosmological Model in General Relativity,” Astrophysics and Space Science, Vol. 317, No. 2, 2008, pp. 21-26.

[20] T. Takabayasi, “Theory of One-Dimensional Relativistic Elastic Continuum for the Model of Particles and Resonances,” Mathematical Physics and Applied Mathematics, Vol. 1, No. 1, 1976, pp. 179-216.

[21] R. Bali and K. Sharma, “Bianchi Type I Bulk Viscous Stiff Fluid Tilted Cosmological Model in General Relativity,” Astrophysics and Space Science, Vol. 275, No. 4, 2001, pp. 485-497.