  Non-rotating neutron stars are generally treated in theoretical studies as
perfect spheres. Such a treatment, however, may not be correct if strong
magnetic fields are present (such as for magnetars) and/or the pressure of the
matter in the cores of neutron stars is non-isotropic (e.g., color
superconducting). In this paper, we investigate the structure of non-spherical
neutron stars in the framework of general relativity. Using a parameterized
metric to model non-spherical mass distributions, we first derive a stellar
structure equation for deformed neutron stars. Numerical investigations of this
model equation show that the gravitational masses of deformed neutron stars
depend rather strongly on the degree and type (oblate or prolate) of stellar
deformation. In particular, we find that the mass of a neutron star increases
with increasing oblateness but decreases with increasing prolateness. If this
feature carries over to a full two-dimensional treatment of deformed neutron
stars, this opens up the possibility that, depending on the type of stellar
deformation, there may exist multiple maximum-mass neutron stars for one and
for the same model for the nuclear equation of state.
