A complete calculation of Shear Viscosity in Strongly Interacting matter

The last observations from the Heavy Ion Collider facilities keep marking new territories in the unexplored field of the high temperature T Quark-Gluon Plasma, with new discoveries that seem to enforce the hypothesis that such an exotic state of Strongly Interacting matter can indeed exist, making it an established fact. Things in the finite baryon density opposite regime are much harder as QCD, and its Lattice formulation, cannot yield any quantitative prediction to date, due to the strong-colour confinement effects in matter at high densities. Nevertheless its behaviour can be inferred from the empirical observations of Neutron Stars, that are sensitive to the composition, and thermodynamical properties of the Nuclear Matter Equation of State. This thesis is focused on the construction of a Hybrid Equation of State, imposing a First-Order colour deconfinement transition of the Second Kind - as pointed out by Lattice QCD studies - between the two phases. Nuclear Matter is described by means of the microscopic Brueckner-Hartree Fock Many Body theory, that builds the in medio properties of interacting nucleons starting from the consistent treatment of realistic Bonn B 2-body vacuum interactions plus effective 3-body forces; Quark Matter is instead treated as a free gas of massless u,d,s quarks with the MIT Bag Model. Shear Viscosity of the strongly interacting Fermi liquid is then calculated in a low-temperature Boltzmann-Landau transport approach, yielding a slight deviation from the Abrikosov-Khalatnikov standard result at quark degrees of freedom dominated densities. The calculations are finally applied to the Astrophysics of Compact Objects: Neutron Stars static configurations are evaluated by means of the relativistic "Tolman-Oppenheimer-Volkoff" structure equations, finding a upper mass limit of 1.81 Solar Masses for the Hybrid Equation of State; furthermore, the estimate of the damping timescales of rotational r-mode Oscillations in Neutron Stars, sensitive to both the Equation of State and to Shear Viscosity of Hybrid Matter, are performed and confronted with the typical Gravitational Radiation instability timescales: the latter dominate in young, cooling Neutron Stars and this could be a promising signal for the LIGO facility, while in old Neutron Stars, at T=0.00001 MeV, the l=m=2 rotational-mode is alone able to suppress the GW emission. Despite the title, the calculation is far from being "complete", but it describes many features in a consistent way supported from the solidity of microscopic calculations of the Strongly Interacting matter properties.