The Effect of a Dark Matter Core on the Structure of a Rotating Neutron Star

Neutron stars represent unique laboratories, offering insights into the physics of supranuclear-density matter and serving as potential hosts for dark matter. This study explores the impact of dark matter cores on rapidly rotating neutron stars through the two-fluid approximation, assuming minimal interaction between baryonic matter and dark matter. The investigation employs phenomenological models for fermionic and bosonic dark matter, revealing that universal relations governing mass and radius changes due to rotation remain largely unaffected in the presence of a dark matter core. Specifically, for a 5 % dark matter mass fraction, the percent deviations in total mass ($M_{tot}$), the baryonic equatorial radius ($R_{Be}$), and polar-to-equatorial baryonic radius ratio ($R_{ratioB}$) are within 3.9 %, 1.8 %, and 1.4 %, respectively. These findings suggest that the universal relations governing neutron star shape can be utilized to infer constraints on the properties of dark matter cores even in cases where the dark matter significantly softens the neutron star's equation of state.