  In this thesis, the effects of the magnetic field on neutron stars matter are
studied, assuming that the neutrons inside these stars are partially or totally
paired forming neutral vector bosons. The main effects of the magnetic field on
the gas are, first, to favor the phase transition to the Bose-Eintein
condensation, and second, to split the pressure in two components, one parallel
and the other perpendicular to the magnetic axis, giving rise to anisotropic
equations of state. At low densities or high magnetic fields, the lowest
pressure can be negative, and the boson system becomes susceptible to suffer a
transverse magnetic collapse. On the other hand, when the temperature is low
enough, the gas can spontaneously magnetize. The equations of state of the
magnetized gas of neutral vector bosons are applied, firstly, to study the
magnetic collpase of an ideal gas of neutrons, electrons and protons (npe gas)
in which the nucleons are partially bosonized. From the results obtained, a
model for the ejection of matter out of the star and the formation of
astrophysical jets is proposed. Subsequently, the equations of state of the
magnetized vector gas are used to study the magnetic field influence on the
structure (mass, radius and deformation) of Bose-Einsten condensate stars, that
is, of compact objects composed entirely by a neutron gas fully bosonized. In
order to appropriately take into account the magnetic anisotropy in the
equations of state of this object, we develope a system of equations to
describe the hydrodynamic equilibrium -- the structure -- of spheroidal compact
objects starting from an axisymmetric metric. The obtained results validate the
bosons self-magnetization as a feasible source for the magnetic field of
compact objects.
