Investigating Neutron Stars through Theory and Simulations

The tidal deformability encodes crucial information about the internal structure and the equation of state of neutron star matter, and plays a fundamental role in the interpretation of gravitational wave signals from binary neutron star systems. This thesis investigates the tidal deformability of non-rotating, unmagnetised neutron stars under the static response approximation, employing a combined approach based on analytical modelling and numerical simulations. The core original contribution of this thesis lies in the development of a computational framework for introducing tidal perturbations within general-relativistic hydrodynamic simulations of isolated neutron stars. The perturbation is implemented in a simplified analytical form, with the primary goal of testing and validating the numerical method. This novel approach enables the study of tidal deformations in a controlled setting, avoiding the complexities associated with full binary dynamics. To validate the scheme, a test simulation of a perturbed neutron star is performed and systematically compared to a benchmark unperturbed case. The comparative analysis reveals a quadrupolar deformation pattern in the perturbed configuration, which qualitatively matches the expected geometry of a tidally deformed object. Although the approximated representation of tidal perturbations limits immediate physical interpretability, the results confirm the validity of the proposed method and demonstrate its potential for future extensions. The computational setup developed in this project is readily adaptable to more complex scenarios, including rotation, strong intrinsic magnetic fields, and more realistic equations of state.