Background: The microscopic composition and properties of infinite hadronic matter at a wide range of densities and temperatures have been subjects of intense investigation for decades. The equation of state (EoS) relating pressure, energy density, and temperature at a given particle number density is essential for modeling compact astrophysical objects such as neutron stars, core-collapse supernovae, and related phenomena, including the creation of chemical elements in the universe. The EoS depends not only on the particles present in the matter, but, more importantly, also on the forces acting among them. Because a realistic and quantitative description of infinite hadronic matter and nuclei from first principles in not available at present, a large variety of phenomenological models has been developed in the past several decades, but the scarcity of experimental and observational data does not allow a unique determination of the adjustable parameters.

In the present work we use the large-$N_c$ approximation to investigate quark matter described by the SU(2) Nambu–Jona-Lasinio model subject to a strong magnetic field. The Landau levels are filled in such a way that usual kinks appear in the effective mass and other related quantities. $\beta$ equilibrium is also considered and the macroscopic properties of a magnetar described by this quark matter is obtained. Our study shows that the magnetar masses and radii are larger if the magnetic field increases but only very large fields ($⩾{10}^{18}$ G) affect the equation of state in a non-negligible way.

In the present work we use the mean-field approximation to investigate quark matter described by the su(3) Nambu–Jona-Lasinio (NJL) model subject to a strong magnetic field. We consider two cases: pure quark matter and quark matter in $\beta$ equilibrium possibly present in magnetars. The results are compared with the ones obtained with the su(2) version of the model. The energy per baryon of magnetized quark matter becomes more bound than nuclear matter made of iron nuclei, for $B$ around $2\times {10}^{19}$ G. When the su(3) NJL model is applied to stellar matter, the maximum mass configurations are always above $1.45M_{\odot }$ and may be as high as $1.86M_{\odot }$ for a central magnetic field of $5\times {10}^{18}$ G. These numbers are within the masses of observed neutron stars.

In the present article we investigate the onset of the pasta phase with different parametrizations of the nonlinear Walecka model. At zero temperature two different methods are used, one based on coexistent phases and the other on the Thomas-Fermi approximation. At finite temperature only the coexistence phases method is used. $\mathit{npe}$ matter with fixed proton fractions and in $\beta$ equilibrium is studied. The pasta phase decreases with the increase of temperature. The internal pasta structure and the beginning of the homogeneous phase vary depending on the proton fraction (or the imposition of $\beta$ equilibrium), on the method used, and on the chosen parametrization. It is shown that a good parametrization of the surface tension with dependence on the temperature, proton fraction, and geometry is essential to describe correctly large isospin asymmetries and the transition from pasta to homogeneous matter.

We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulas appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations $\Omega =-P_{\parallel }$ and $P_{\perp }=P_{\parallel }-MB$, with $M=-\partial \Omega /\partial B$ being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.

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