Magnetised Dense Nuclear Matter in Neutron Stars: A Relativistic Mean-Field Study of the Equation of State

We study the static response of dense neutron-star matter to a prescribed magnetic-field strength within a deliberately minimal and internally consistent relativistic mean-field (RMF) baseline. The model includes neutrons, protons, electrons, and muons in beta equilibrium and charge neutrality, with a uniform external magnetic field incorporated through Landau quantisation of the charged species. The equation of state is evaluated self-consistently at zero temperature, while moderate finite-temperature effects are estimated through leading-order degenerate Sommerfeld corrections. Magnetic pressure anisotropy is included through the Maxwell contribution in the no-magnetisation approximation. The purpose of this baseline is to isolate the hierarchy of magnetic-field effects before introducing additional microphysics or dynamical magnetic-field evolution. We compare the linear QHD-I parameterisation, used as a stiff benchmark, with the nonlinear GM1 model as a more realistic reference. The results show that canonical magnetar-scale fields produce negligible changes in the bulk core equation of state, while visible Landau-quantisation and pressure-anisotropy effects emerge only as the field approaches the strongly quantising regime. The comparison between QHD-I and GM1 further shows that nuclear-model dependence dominates over static magnetic-field corrections up to the field strengths explored here. As an exploratory diagnostic, we use the isotropised equation of state to estimate the sensitivity of ordinary TOV mass–radius sequences to the prescribed magnetic field. This should not be interpreted as a fully anisotropic magnetised-star calculation. Anomalous magnetic moments, hyperons, quark degrees of freedom, and dynamical magnetic-field evolution are left for future extensions.