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

Quark matter under strong magnetic fields in the Nambu--Jona-Lasinio Model