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New Class of Magnetized Inhomogeneous Bianchi Type-I Cosmological Model with Variable Magnetic Permeability in Lyra Geometry

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Abstract

Inhomogeneous Bianchi type-I cosmological model with electro-magnetic field based on Lyra geometry is investigated. Using separated method, the Einstein field equations have been solved analytically with the aid of Mathematica program. A new class of exact solutions have been obtained by considering the potentials of metric and displacement field are functions of coordinates t and x. We have assumed that F 12 is the only non-vanishing component of electro-magnetic field tensor F ij . The Maxwell’s equations show that F 12 is the function of x alone whereas the magnetic permeability is the function of x and t both. To get the deterministic solution, it has been assumed that the expansion scaler Θ in the model is proportional to the value \(\sigma_{1}^{1}\) of the shear tensor \(\sigma_{i}^{j}\). Some physical and geometric properties of the model are also discussed and graphed.

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Authors and Affiliations

  1. Faculty of Science, Department of Mathematics, King Abdul Aziz University, P.O. Box 80203, Jeddah, 21589, Saudi Arabia

    Ahmad T. Ali

  2. Mathematics Department, Faculty of Science, Al-Azhar University, Nasr City, 11884, Cairo, Egypt

    Ahmad T. Ali

  3. Department of Mathematics, Jadavpur University, Kolkata, 700 032, West Bengal, India

    F. Rahaman

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  1. Ahmad T. Ali
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  2. F. Rahaman
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Correspondence to F. Rahaman.

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Ali, A.T., Rahaman, F. New Class of Magnetized Inhomogeneous Bianchi Type-I Cosmological Model with Variable Magnetic Permeability in Lyra Geometry. Int J Theor Phys 52, 4055–4067 (2013). https://doi.org/10.1007/s10773-013-1719-8

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  • DOI: https://doi.org/10.1007/s10773-013-1719-8

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