Five Dimensional String Universes in Lyra Manifold
Affiliation(s)
1 Department of Mathematics, Commerce College Kokrajhar, Kokrajhar, BTC, Assam, India. 2 Department of Mathematical Sciences, Bodoland University, Kokrajhar, BTC, Assam, India. 3 Department of Mathematics Sciences, National Institute of Technology Manipur, Imphal, India.
1 Department of Mathematics, Commerce College Kokrajhar, Kokrajhar, BTC, Assam, India. 2 Department of Mathematical Sciences, Bodoland University, Kokrajhar, BTC, Assam, India. 3 Department of Mathematics Sciences, National Institute of Technology Manipur, Imphal, India.
ABSTRACT
Considering five dimensional plane symmetric metric, we discuss a model universe with different situations, by solving the modified Einstein field equations within the framework of Lyra geometry. We obtain many interesting realistic solutions governing the present day model of the universe. Physical and kinematical properties of the models are discussed in detail.
Considering five dimensional plane symmetric metric, we discuss a model universe with different situations, by solving the modified Einstein field equations within the framework of Lyra geometry. We obtain many interesting realistic solutions governing the present day model of the universe. Physical and kinematical properties of the models are discussed in detail.
Cite this paper
Mollah, M. , Singh, K. and Singh, K. (2015) Five Dimensional String Universes in Lyra Manifold. International Journal of Astronomy and Astrophysics, 5, 90-94. doi: 10.4236/ijaa.2015.52012.
Mollah, M. , Singh, K. and Singh, K. (2015) Five Dimensional String Universes in Lyra Manifold. International Journal of Astronomy and Astrophysics, 5, 90-94. doi: 10.4236/ijaa.2015.52012.
References
[1] Weyl, H. (1918) Sitzungsberichte Der Preussischen Akademie Der Wissenschaften. Academy Wiss, Berlin, 465. [2] Lyra, G. (1951) über-eine Modifikation der Riemannschen Geometrie. Mathematische Zeitschrift, 54, 52-64.
http://dx.doi.org/10.1007/BF01175135 [3] Pradhan, A. and Kumar, S.S. (2009) Plane Symmetric Inhomogeneous Perfect Fluid Universe with Electromagnetic Field in Lyra Geometry. Astrophysics and Space Science, 321, 137-146.
http://dx.doi.org/10.1007/s10509-009-0015-9 [4] Pradhan, A. and Mathur, P. (2009) Inhomogeneous Perfect Fluid Universe with Electromagnetic Field in Lyra Geometry. Fizika B, 18, 243-264. (gr-qc/0806.4815) [5] Pradhan, A. and Yadav, P. (2009) Accelerated Lyra’s Cosmology Driven by Electromagnetic Field in Inhomogeneous Universe. International Journal of Mathematics and Mathematical Sciences (IJMMS), 2009, Article ID: 471938, 20 p.
http://dx.doi.org/10.1155/2009/471938 [6] Pradhan, A. (2009) Cylindrically Symmetric Viscous Fluid Universe in Lyra Geometry. Journal of Mathematical Physics, 50, 022501-022513.
http://dx.doi.org/10.1063/1.3075571 [7] Pradhan, A., Amirhashchi, H. and Zainuddin, H. (2011) A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold. International Journal of Theoretical Physics, 50, 56-69.
http://dx.doi.org/10.1007/s10773-010-0493-0 [8] Pradhan, A. and Singh, A.K. (2011) Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter. International Journal of Theoretical Physics, 50, 916-933.
http://dx.doi.org/10.1007/s10773-010-0636-3 [9] Yadav, A.K. (2010) Lyra’s Cosmology of Inhomogeneous Universe with Electromagnetic Field. Fizika B, 19, 53-80. [10] Agarwal, S., Pandey, R and Pradhan, A. (2011) LRS Bianchi Type II Perfect Fluid Cosmological Models in Normal Gauge for Lyra’s Manifold. International Journal of Theoretical Physics, 50, 296-307.
http://dx.doi.org/10.1007/s10773-010-0523-y [11] Singh, R.S. and Singh, A. (2012) A New Class of Magnetized Inhomogeneous Cosmological Models of Perfect Fluid Distribution with Variable Magnetic Permiability in Lyra Geometry. Electronic Journal of Theoretical Physics, 9, 265-282. [12] Bhamra, K.S. (1974) A Cosmological Model of Class One in Lyra’s Manifold. Australian Journal of Physics, 27, 541-547.
http://dx.doi.org/10.1071/PH740541 [13] Kalyanshetti, S.B. and Waghmode, B.B. (1982) A Static Cosmological Model in Einstein-Cartan Theory. General Relativity and Gravitation, 14, 823-830. [14] Soleng, H.H. (1987) Cosmologies Based on Lyra’s Geometry. General Relativity and Gravitation, 19, 1213-1216. [15] Sen, D.K. and Vanstone, J.R. (1972) On Weyl and Lyra Manifolds. Journal of Mathematical Physics, 13, 990-994.
http://dx.doi.org/10.1063/1.1666099 [16] Karade, T.M. and Borikar, S.M. (1978) Thermodynamic Equilibrium of a Gravitating Sphere in Lyra’s Geometry. General Relativity and Gravitation, 9, 431-436. [17] Reddy, D.R.K. and Innaiah, P. (1986) A Plane Symmetric Cosmological Model in Lyra Manifold. Astrophysics and Space Science, 123, 49-52.
http://dx.doi.org/10.1007/BF00649122 [18] Reddy, D.R.K. and Venkateswarlu, R. (1987) Birkhoff-Type Theorem in the Scale Covariant Theory of Gravitation. Astrophysics and Space Science, 136, 191-194. [19] Asgar, A. and Ansary, M. (2014) Accelerating Bianchi Type-VI0 Bulk Viscous Cosmological Models in Lyra Geometry. Journal of Theoretical and Applied Physics, 8, 219-224.
http://dx.doi.org/10.1007/s40094-014-0151-7 [20] Kumari, P., Singh, M.K. and Ram, S. (2013) Anisotropic Bianchi Type-III Bulk Viscous Fluid Universe in Lyra Geometry. Advances in Mathematical Physics, 2013, Article ID: 416294.
http://dx.doi.org/10.1155/2013/416294 [21] Asgar, A. and Ansary, M. (2014) Bianchi Type-V Universe with Anisotropic Dark Energy in Lyra’s Geometry. The African Review of Physics, 9, 145-151. [22] Zia, R. and Singh, R.P. (2012) Bulk Viscous Inhomogeneous Cosmological Models with Electromagnetic Field in Lyra Geometry. Romanian Journal of Physics, 57, 761-778. [23] Asgar, A. and Ansary, M. (2014) Exact Solutions of Axially Symmetric Bianchi Type-I Cosmological Model in Lyra Geometry. IOSR Journal of Applied Physics (IOSR-JAP), 5, 1-5.
www.iosrjournals.org [24] Panigrahi, U.K. and Nayak, B. (2014) Five Dimensional Stiff Fluids with Variable Displacement Vector in Lyra Manifold. International Journal of Mathematical Archive, 5, 123-128.
www.ijma.info [25] Halford, W.D. (1970) Cosmological Theory Based on Lyra’s Geometry. Australian Journal of Physics, 23, 863-869.
http://dx.doi.org/10.1071/PH700863 [26] Halford, W.D. (1972) Scalar-Tensor Theory of Gravitation in a Lyra Manifold. Journal of Mathematical Physics, 13, 1699-1703.
http://dx.doi.org/10.1063/1.1665894
[1] Weyl, H. (1918) Sitzungsberichte Der Preussischen Akademie Der Wissenschaften. Academy Wiss, Berlin, 465. [2] Lyra, G. (1951) über-eine Modifikation der Riemannschen Geometrie. Mathematische Zeitschrift, 54, 52-64.
http://dx.doi.org/10.1007/BF01175135 [3] Pradhan, A. and Kumar, S.S. (2009) Plane Symmetric Inhomogeneous Perfect Fluid Universe with Electromagnetic Field in Lyra Geometry. Astrophysics and Space Science, 321, 137-146.
http://dx.doi.org/10.1007/s10509-009-0015-9 [4] Pradhan, A. and Mathur, P. (2009) Inhomogeneous Perfect Fluid Universe with Electromagnetic Field in Lyra Geometry. Fizika B, 18, 243-264. (gr-qc/0806.4815) [5] Pradhan, A. and Yadav, P. (2009) Accelerated Lyra’s Cosmology Driven by Electromagnetic Field in Inhomogeneous Universe. International Journal of Mathematics and Mathematical Sciences (IJMMS), 2009, Article ID: 471938, 20 p.
http://dx.doi.org/10.1155/2009/471938 [6] Pradhan, A. (2009) Cylindrically Symmetric Viscous Fluid Universe in Lyra Geometry. Journal of Mathematical Physics, 50, 022501-022513.
http://dx.doi.org/10.1063/1.3075571 [7] Pradhan, A., Amirhashchi, H. and Zainuddin, H. (2011) A New Class of Inhomogeneous Cosmological Models with Electromagnetic Field in Normal Gauge for Lyra’s Manifold. International Journal of Theoretical Physics, 50, 56-69.
http://dx.doi.org/10.1007/s10773-010-0493-0 [8] Pradhan, A. and Singh, A.K. (2011) Anisotropic Bianchi Type-I String Cosmological Models in Normal Gauge for Lyra’s Manifold with Constant Deceleration Parameter. International Journal of Theoretical Physics, 50, 916-933.
http://dx.doi.org/10.1007/s10773-010-0636-3 [9] Yadav, A.K. (2010) Lyra’s Cosmology of Inhomogeneous Universe with Electromagnetic Field. Fizika B, 19, 53-80. [10] Agarwal, S., Pandey, R and Pradhan, A. (2011) LRS Bianchi Type II Perfect Fluid Cosmological Models in Normal Gauge for Lyra’s Manifold. International Journal of Theoretical Physics, 50, 296-307.
http://dx.doi.org/10.1007/s10773-010-0523-y [11] Singh, R.S. and Singh, A. (2012) A New Class of Magnetized Inhomogeneous Cosmological Models of Perfect Fluid Distribution with Variable Magnetic Permiability in Lyra Geometry. Electronic Journal of Theoretical Physics, 9, 265-282. [12] Bhamra, K.S. (1974) A Cosmological Model of Class One in Lyra’s Manifold. Australian Journal of Physics, 27, 541-547.
http://dx.doi.org/10.1071/PH740541 [13] Kalyanshetti, S.B. and Waghmode, B.B. (1982) A Static Cosmological Model in Einstein-Cartan Theory. General Relativity and Gravitation, 14, 823-830. [14] Soleng, H.H. (1987) Cosmologies Based on Lyra’s Geometry. General Relativity and Gravitation, 19, 1213-1216. [15] Sen, D.K. and Vanstone, J.R. (1972) On Weyl and Lyra Manifolds. Journal of Mathematical Physics, 13, 990-994.
http://dx.doi.org/10.1063/1.1666099 [16] Karade, T.M. and Borikar, S.M. (1978) Thermodynamic Equilibrium of a Gravitating Sphere in Lyra’s Geometry. General Relativity and Gravitation, 9, 431-436. [17] Reddy, D.R.K. and Innaiah, P. (1986) A Plane Symmetric Cosmological Model in Lyra Manifold. Astrophysics and Space Science, 123, 49-52.
http://dx.doi.org/10.1007/BF00649122 [18] Reddy, D.R.K. and Venkateswarlu, R. (1987) Birkhoff-Type Theorem in the Scale Covariant Theory of Gravitation. Astrophysics and Space Science, 136, 191-194. [19] Asgar, A. and Ansary, M. (2014) Accelerating Bianchi Type-VI0 Bulk Viscous Cosmological Models in Lyra Geometry. Journal of Theoretical and Applied Physics, 8, 219-224.
http://dx.doi.org/10.1007/s40094-014-0151-7 [20] Kumari, P., Singh, M.K. and Ram, S. (2013) Anisotropic Bianchi Type-III Bulk Viscous Fluid Universe in Lyra Geometry. Advances in Mathematical Physics, 2013, Article ID: 416294.
http://dx.doi.org/10.1155/2013/416294 [21] Asgar, A. and Ansary, M. (2014) Bianchi Type-V Universe with Anisotropic Dark Energy in Lyra’s Geometry. The African Review of Physics, 9, 145-151. [22] Zia, R. and Singh, R.P. (2012) Bulk Viscous Inhomogeneous Cosmological Models with Electromagnetic Field in Lyra Geometry. Romanian Journal of Physics, 57, 761-778. [23] Asgar, A. and Ansary, M. (2014) Exact Solutions of Axially Symmetric Bianchi Type-I Cosmological Model in Lyra Geometry. IOSR Journal of Applied Physics (IOSR-JAP), 5, 1-5.
www.iosrjournals.org [24] Panigrahi, U.K. and Nayak, B. (2014) Five Dimensional Stiff Fluids with Variable Displacement Vector in Lyra Manifold. International Journal of Mathematical Archive, 5, 123-128.
www.ijma.info [25] Halford, W.D. (1970) Cosmological Theory Based on Lyra’s Geometry. Australian Journal of Physics, 23, 863-869.
http://dx.doi.org/10.1071/PH700863 [26] Halford, W.D. (1972) Scalar-Tensor Theory of Gravitation in a Lyra Manifold. Journal of Mathematical Physics, 13, 1699-1703.
http://dx.doi.org/10.1063/1.1665894