Differentially rotating neutron stars with dark matter cores

Dark matter is expected to accumulate inside neutron stars, modifying the structure of isolated stars and influencing both the dynamics of binary mergers and the evolution of the resulting hypermassive remnants. Since differential rotation is the primary mechanism delaying the collapse of these remnants, understanding its behavior is crucial when assessing the impact of an embedded dark component. In this work, we extend the numerical code to describe two gravitationally coupled fluids in differential rotation, with baryonic matter modeled by a realistic nuclear equation of state and dark matter represented as a self-interacting bosonic condensate. Restricting the models to the zero-temperature approximation, we focus on the internal equilibrium structure. Within this framework, we construct equilibrium sequences for a representative differential rotation law, providing a basis to explore how dark matter may influence the global properties and rotational dynamics of binary neutron star remnants.