Numerical modelling of dark matter-admixed compact objects

This thesis explores how dark matter might reveal itself through the structure and dynamics of compact stars. A unified framework in which ordinary matter and a self-interacting dark component coexist inside the same star is developed, influencing each other only through gravity. Within this setting three connected problems are studied: compact objects made entirely of dark matter; rapidly rotating neutron stars that contain a dark component; and differentially rotating remnants that resemble the aftermath of neutron-star mergers. Methodologically, the work extends the RNS code to handle two fluids that can rotate differently. This allows a systematic scan of plausible configurations and a clean comparison with standard one-fluid neutron star models. Even modest amounts of dark matter can shift global stellar properties in ways that resemble changes in the nuclear equation of state. Mass-radius relations, tidal deformability, and moments of inertia are all affected, and the imprint depends on how the dark component is distributed and rotates. These trends create degeneracies that single measurements cannot resolve, but they also open new opportunities: combining gravitational-wave observations, X-ray timing, and late-time post-merger signals offers a realistic path to distinguish dark-matter effects from purely hadronic physics. Overall, the thesis indicates that allowing for a dark component can be important for obtaining unbiased inferences about dense matter, especially in environments where dark-matter accumulation is plausible. At the same time, compact stars emerge as potential laboratories for the dark sector: by tracing how their observable properties react to a hidden fluid, the results outline targets for future multimessenger searches.