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Abstract We present the implementation of a two-moment-based general-relativistic multigroup radiation transport module in theGeneral-relativisticmultigridnumerical (Gmunu) code. On top of solving the general-relativistic magnetohydrodynamics and the Einstein equations with conformally flat approximations, the code solves the evolution equations of the zeroth- and first-order moments of the radiations in the Eulerian-frame. An analytic closure relation is used to obtain the higher order moments and close the system. The finite-volume discretization has been adopted for the radiation moments. The advection in spatial space and frequency-space are handled explicitly. In addition, the radiation–matter interaction terms, which are very stiff in the optically thick region, are solved implicitly. The implicit–explicit Runge–Kutta schemes are adopted for time integration. We test the implementation with a number of numerical benchmarks from frequency-integrated to frequency-dependent cases. Furthermore, we also illustrate the astrophysical applications in hot neutron star and core-collapse supernovae modelings, and compare with other neutrino transport codes. 

Abstract Highly magnetized neutron stars are promising candidates to explain some of the most peculiar astronomical phenomena, for instance, fast radio bursts, gamma-ray bursts, and superluminous supernovae. Pulsations of these highly magnetized neutron stars are also speculated to produce detectable gravitational waves. In addition, pulsations are important probes of the structure and equation of state of the neutron stars. The major challenge in studying the pulsations of highly magnetized neutron stars is the demanding numerical cost of consistently solving the nonlinear Einstein and Maxwell equations under minimum assumptions. With the recent breakthroughs in numerical solvers, we investigate pulsation modes of non-rotating neutron stars which harbour strong purely toroidal magnetic fields of 10¹⁵⁻¹⁷G through two-dimensional axisymmetric general-relativistic magnetohydrodynamics simulations. We show that stellar oscillations are insensitive to magnetization effects until the magnetic to binding energy ratio goes beyond 10%, where the pulsation mode frequencies are strongly suppressed. We further show that this is the direct consequence of the decrease in stellar compactness when the extreme magnetic fields introduce strong deformations of the neutron stars.