Inhomogeneity in the Mass Distribution of Deformed Neutron Stars

Non-rotating neutron stars with high magnetic fields and/or neutron stars containing color-superconducting quark matters cores break traditional spherical symmetry, thus resulting these objects to be oblong spheroids with distinct polar and equatorial directions. The mass distribution is then expected to be non-homogeneous thus resulting in a non-zero mass quadrupole moment. Recent publications on the stellar structure of deformed neutron stars suggest the mass could significantly change depending on the type of deformation. In this work, we investigate the mass distribution of deformed neutron stars in the framework of general relativity by numerically calculating the gravitational mass quadrupole moment and study its effects on the stellar structure of these deformed objects.