Anisotropic Compact Stars: Theory and Simulation from Microphysical Models to Macroscopic Structure and Observables

Strong magnetic fields and anisotropic stresses can substantially modify the structure and observable properties of compact stars. In this review, we present a unified treatment of magnetically induced anisotropy across neutron stars, hybrid stars, and white dwarfs, connecting the microphysical equation of state effects to macroscopic structure and multimessenger observables. We demonstrate that magnetic-field geometry plays a decisive role: toroidally oriented (transverse) fields enhance the maximum mass by providing additional perpendicular pressure support, whereas radially oriented fields primarily increase central compression with comparatively small mass gain. In neutron stars, anisotropy and magnetic stresses can shift phase-transition thresholds in hybrid models and enable configurations in the lower mass gap with significantly smaller magnetic energy compared to the gravitational binding energy. We further show that continuous gravitational wave emission from magnetically deformed neutron stars provides a complementary probe of internal field geometry through ellipticity-driven strain evolution. In magnetized white dwarfs, super-Chandrasekhar masses arise from the spatial redistribution of magnetic stresses rather than from globally strong magnetic energy. Taken together, these results highlight that magnetic-field geometry and matter anisotropy are as important as field strength in determining mass–radius relations, tidal deformability, gravitational wave detectability, and the emergence of extreme compact-star configurations.