Anisotropic pressure in dense neutron matter under the presence of a strong magnetic field

Dense neutron matter with recently developed BSk19 and BSk21 Skyrme effective forces is considered in magnetic fields up to ${10}^{20}$ G at zero temperature. The breaking of the rotational symmetry by the magnetic field leads to the differentiation between the pressures along and perpendicular to the field direction which becomes significant in the fields $H>H_{th}\sim {10}^{18}$ G. The longitudinal pressure vanishes in the critical field ${10}^{18}<H_c\lesssim {10}^{19}$ G, resulting in the longitudinal instability of neutron matter. For the Skyrme force fitted to the stiffer underlying equation of state (BSk21 vs. BSk19) the threshold $H_{th}$ and critical $H_c$ magnetic fields become larger. The longitudinal and transverse pressures as well as the anisotropic equation of state of neutron matter are determined under the conditions relevant for the cores of magnetars.