We investigate the effects of strong magnetic fields on the equation of state of warm stellar matter as it may occur in a protoneutron star. Both neutrino free and neutrino trapped matter at a fixed entropy per baryon are analyzed. A relativistic mea
n field nuclear model, including the possibility of hyperon formation, is considered. A density dependent magnetic field with the magnitude $10^{15}$ G at the surface and not more than $3times 10^{18}$ G at the center is considered. The magnetic field gives rise to a neutrino suppression, mainly at low densities, in matter with trapped neutrinos. It is shown that an hybrid protoneutron star will not evolve to a low mass blackhole if the magnetic field is strong enough and the magnetic field does not decay. However, the decay of the magnetic field after cooling may give rise to the formation of a low mass blackhole.
We study the effect of a strong magnetic field on the properties of neutron stars with a quark-hadron phase transition. It is shown that the magnetic field prevents the appearance of a quark phase, enhances the leptonic fraction, decreases the baryon
ic density extension of the mixed phase and stiffens the total equation of state, including both the stellar matter and the magnetic field contributions. Two parametrisations of a density dependent static magnetic field, increasing, respectively, fast and slowly with the density and reaching $2-4times 10^{18}$G in the center of the star, are considered. The compact stars with strong magnetic fields have maximum mass configurations with larger masses and radius and smaller quark fractions. The parametrisation of the magnetic field with density has a strong influence on the star properties.
