Consequences of Axial Symmetry on Compact Stellar Objects*

Compact objects with high magnetic fields such as magnetars and/or neutron stars, which may contain color-superconducting quark matter cores can break from standard spherical symmetry and are expected to be deformed, making them oblong spheroids with distinct polar and equatorial radii. Recent studies on the stellar structure of these deformed stars indicate that the mass could either increase or decrease depending on the shape of these objects. Thus, due to these deformations, the gravitational quadrupole moment (mass distribution) of these compact stars is not homogeneous and is expected to be non-zero. In this work, we examine this inhomogeneity by computing the gravitational mass quadrupole moment of non-rotating deformed neutron stars in the framework of general relativity and investigate any changes from conventional spherical models.