I have tried to investigate an anisotropic cosmological model within General Relativity, featuring a magneto-hydrodynamics (MHD) Fluid by derive the evolution equations. This work mainly depends on investigates a cosmological model of an anisotropic universe described by General Relativity, in corporating the effects of a homogeneous magnetic field using covariant magneto-hydrodynamics. I have explored exact solutions to the field equations, often using specific anisotropic metrics to analyze the evolution of shear, expansion and magnetic field generation. Here, we present a detailed mathematical equations study of an anisotropic universe governed by the laws of general relativity in the presence of a large scale magnetic field.
Mantu Kumar (Tue,) studied this question.
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