Dissipative and shearing dynamics in astrophysical compact objects

Binary neutron star mergers represent unique observational phenomena because all four fundamental interactions play an important role at various stages of their evolution by leaving imprints in astronomical observables. This makes their accurate numerical modeling a challenging multiphysics problem that promises to increase our understanding of the high-energy astrophysics at play, thereby providing constraints for the underlying fundamental theories such as the gravitational interaction or the strong interaction of dense matter. For example, the first and so far only multi-messenger observation of the binary neutron star merger GW170817 resulted in numerous bounds on the parameters of isolated non-rotating neutron stars, e.g., their maximum mass or their distribution in radii, which can be directly used to constrain the equation of state of cold nuclear matter. While many of these results stem from the observation of the inspiral gravitational-wave signal, the postmerger phase of binary neutron star mergers encodes even more details about the extreme physics of hot and dense neutron star matter. In this Thesis we focus on the exploration of dissipative and shearing effects in binary neutron star mergers in order to identify novel approaches to constrain hot and dense neutron star matter. The first effect is the well-motivated dissipation of energy due to the bulk viscosity which arises from violations of weak chemical equilibrium. We start by exploring the impact of bulk viscosity on black-hole accretion. This simplified problem gives us the opportunity to develop a test case for future codes taking into account the effects of dissipation in a fully general-relativistic setup and build intuition in the physics of relativistic dissipation. Next, we move on to isolated neutron stars and binary neutron star mergers by developing a robust implementation of bulk-viscous dissipation for numerical relativity simulations. We test our implementation by calculating the damping of eigenmodes of isolated neutron stars and the violent migration scenario. Finally, we present the first results on the impact of bulk viscosity on binary neutron star mergers. We identify a number of ways how bulk viscosity impacts the postmerger phase, out of which the suppression of gravitational-wave emission and dynamical mass ejection are the most notable ones. In the last part of this Thesis we investigate how the shearing dynamics at the beginning of the merger affects the amplification of different initial magnetic-field topologies. We explore the hypothesis that magnetic fields which are located only in a small region near the stellar surface prior to merger lead to a weaker magnetic-field amplification. We show first evidence which confirms this hypothesis and discuss possible implications for constraining the physics of superconduction in cold neutron stars.