Simulazioni della Coalescenza di Stelle di Neutroni Binarie nell'Era dell'Astrofisica Multimessaggera

The recent ground-breaking detection of gravitational waves (GW) from the merger of two neutron stars (NS), known as the GW170817 event, along with the observations of electromagnetic counterparts across the entire spectrum including a short gamma-ray burst (SGRB) and a radioactively powered kilonova, has given birth to the era of multimessenger astrophysics with GW sources. In order to probe the underlying physical mechanisms at play in such systems, it is necessary to employ fully general relativistic magnetohydrodynamic (GRMHD) simulations, including effects of magnetic fields and neutrino emission/reabsorption for a more realistic description. In the first part of this Thesis, we introduce our newly-developed GRMHD code Spritz, that solves the GRMHD equations in 3D Cartesian coordinates and on a dynamical spacetime. We present its salient features including the staggered formulation of the vector potential as well as support for any arbitrary equation of state (EOS), followed by a series of tests for code validation. We then describe the implementation of an approximate neutrino leakage scheme in Spritz, shedding some light on the involved equations, physical assumptions, and implemented numerical methods including higher order schemes, along with a large battery of general relativistic tests performed with and without magnetic fields and/or neutrino leakage. Since flux-conserving GRMHD codes like Spritz depend upon a technical algorithm to recover the fundamental `primitive' variables from the evolved `conserved' ones, which is often error-prone, we propose a new robust, accurate and efficient conservative-to-primitive variable recovery scheme named `RePrimAnd', along with the proof of existence of a solution and its uniqueness. As a next natural step, we implemented this scheme in Spritz, and performed a number of demanding GRMHD tests including critical cases like a NS collapse to a black hole (BH) as well as the evolution of a BH-accretion disk system. The second part of the thesis focusses instead on the application of GRMHD codes to perform magnetized BNS merger simulations. In particular, using the WhiskyMHD code, we present a detailed study of BNS merger simulations forming a long-lived NS remnant and including long post-merger evolution. Exploring this `magnetar scenario' allows us to address some of the open questions in the context of the SGRB and accompanying kilonova of the GW170817 event. Finally, we also discuss the results of the first magnetized BNS merger simulation performed with Spritz and the RePrimAnd scheme, concluding with an outlook on the next steps.