Abstract
Generally, over the last 75 years, since the publication of the well known papers from from R. C. Tolman (Tolman 1939) and J. R. Oppenheimer and G. M. Volkoff (Oppenheimer and Volkoff 1939), standard models of non-rotating neutron stars are modeled with the assumption that they are perfect spheres. This assumption of perfect spherical symmetry is not correct if the matter inside of neutron stars is described by a non-isotropic equation of state (EoS). Particular classes of neutron stars such as Magnetars and neutron stars that contain color superconducting quark matter cores are expected to be deformed making them oblong spheroids. In this paper, we examine the deformity of these non-spherical neutron stars by deriving the stellar structure equations in the framework of general relativity. Using a non-isotropic model for the equation of state, these stellar structure equations are solved numerically in two dimensions. We then calculate stellar properties such as masses and radii along with pressure and energy-density profiles and investigate any changes from conventional spherical models.
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