Bianchi type-III non-static magnetized cosmological model for perfect fluid distribution in general relativity

Abstract

We have investigated Bianchi type III non-static magnetized cosmological model for perfect fluid distribution in general relativity. We assume that F ₁₂ is the only non-vanishing component of F _ij . Maxwell’s equation

$$\frac{\partial}{\partial {x}^{j}}\bigl(F_{{ij}}\sqrt{-g}\bigr)=0$$

leads to

$${F}_{12}=\mathrm{Ke}^{-\alpha {x}}$$

where K and α are constants.

To get a deterministic model, we assume that σ ¹₁ ∝ θ which leads to A=C ⁿ where n is a constant, σ ₁₁ the x-component of shear tensor σ _ij and theta is the expansion in the model. The behaviour of the model in absence of magnetic field is discussed. The other physical and geometrical aspects of the model are also discussed.