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

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 F12 is the only non-vanishing component of electro-magnetic field tensor Fij. 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 σ11 of the shear tensor σij. Some physical and geometric properties of the model are also discussed and graphed. © 2013 Springer Science+Business Media New York.