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

TL;DR

This paper develops a new class of exact solutions for an inhomogeneous Bianchi type-I cosmological model within Lyra geometry, incorporating variable magnetic permeability and electromagnetic fields, analyzed through analytical and computational methods.

Contribution

It introduces a novel class of solutions considering variable magnetic permeability and electromagnetic fields in Lyra geometry, expanding understanding of inhomogeneous cosmological models.

Findings

Derived exact solutions for the Einstein field equations in Lyra geometry.

Analyzed the physical and geometric properties of the model.

Explored the effects of variable magnetic permeability on cosmological evolution.

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.