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

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 I similar to in the model is proportional to the value of the shear tensor . Some physical and geometric properties of the model are also discussed and graphed.