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 programm. 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 Maxwells 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 Theta in the model is proportional to the value sigma(11) of the shear tensor sigma(ij). Some physical and geometric properties of the model are also discussed and graphed.