The fact that a magnetic field in a fermion system breaks the spherical symmetry suggest that the intrinsic geometry of this system is axisymmetric rather than spherical. In this work we analyze the impact of anisotropic pressures, due to the presenc
e of a magnetic field, in the structure equations of a magnetized quark star. We assume a cylindrical metric and an anisotropic energy momentum tensor for the source. We found that there is a maximum magnetic field that the star can sustain, closely related to the violation of the virial relations.
We investigate the quantum corrections of the anomalous magnetic moment (AMM) for fermions in the presence of a strong magnetic field using the Rituss approach. At strong fields the particles get different AMMs depending on the LLs. This result is di
fferent from what is obtained with the Schwingers approximation at weak field where the AMM is independent of the LL. We analyze the significance of the AMM contribution to the Equation of State (EoS) of the magnetized system, in the weak and strong field approximations.
