Andrea Sabatucci

Neutron stars are long known to provide a unique environment to investigate the properties of cold and dense nuclear matter. The detection of the first gravitational wave signal coming from a binary neutron star merger (GW170817) offered a valuable new source of information, marking the rise of the multimessenger astronomy era. Among the various theoretical approaches attempting to describe nuclear matter, non-relativistic nuclear many-body theory has proven to be extremely consistent and to have a remarkable predictive power. In this seminar, we discuss the role of relativistic corrections within this framework and their interplay with three-nucleon forces. The introduction of relativistic boost corrections to the nucleon-nucleon potential entails a reduction of the three-nucleon repulsion, resulting into a softening of the equation of state at high density. We present the results of a Bayesian analysis aimed at constraining the strength of a phenomenological three-nucleon repulsive potential with multimessenger neutron star data. This analysis highlighted the strong sensitivity of neutron star observables to small variations in the strength of the three-nucleon repulsion. Nevertheless, it also showed how current astrophysical data still lack the accuracy to put stringent constraints. Therefore, an extension aimed at exploring the potential of the Einstein Telescope, a designed third-generation gravitational wave detector, is also presented. Finally, we introduce the formalism of the Correlated Basis Function Effective Interaction and discuss its extension to include relativistic corrections. This approach has proven highly efficient in computing properties beyond the equation of state, such as single-particle properties and transport coefficients.