Efecto del campo magnético en estrellas de bosones escalares cargados

We study the structure and properties of Bose-Einstein Condensate (BEC) Stars as alternatives to conventional neutron stars. The work focuses on the thermodynamic study of gases composed of charged scalar bosons and fermions (electrons, protons, and neutrons) under a uniform magnetic field, paying particular attention to the low-temperature limit. Expressions are derived for the thermodynamic potential, particle densities, energies, anisotropic pressures, and magnetization, including both statistical and vacuum contributions, with the latter separated into the contribution from the Lowest Landau Level (LLL) and excited levels. Based on these results, anisotropic equations of state (EoS) are constructed that incorporate chemical equilibrium and charge neutrality conditions for a mixed \textit{npe}+$π^-$ gas. These EoS are then implemented in a system of anisotropic structure equations based on an axisymmetric metric, allowing for the analysis of how the magnetic field modifies the structure of BEC stars, including their masses, radii, deformations, gravitational redshifts, and mass quadrupole moments. Numerical results are presented showing the influence of the magnetic field on the global properties of these stars, including potential observable signatures.