Anisotropic models in magnetized Bianchi Type-III spacetimes via noether symmetries

This research paper is two-fold. In the first part, we study Noether and Killing symmetries in Bianchi Type-III spacetimes, along with the associated conservation laws. The study uses the Maple RIFSIMP package to transform a set of nonlinear differential equations into a simpler form called the reduced involutive form (RIF). This method generates a RIF tree, where each branch is solved to find the explicit forms of Noether symmetries. We also examine the Noether symmetry related to homothety and analyze this symmetry separately within each group. In the second part, we investigate the behavior of an anisotropic fluid under the influence of a magnetic field, which is assumed to be aligned along the z-axis. The anisotropic fluid model is consistent with the inherent anisotropy of Bianchi Type-III, which may be amplified by the presence of the magnetic field. We also study how this magnetic field affects the fluid’s physical properties and explore the conditions under which the fluid may approach isotropy.