Towards relativistic hydrodynamics with spin currents

In this thesis, some aspects of hydrodynamics on systems with non-trivial spin degrees of freedom are studied. We start by identifying the relevant spin degrees of freedom and how they can be incorporated in the hydrodynamic expansion. After this has been achieved we modify the constitutive relations to include such degrees of freedom, this is done in a way compatible with the second law of thermodynamics. Conformal symmetry in the presence of spin degrees of freedom is also analyzed and is used to write down an idealized model that resembles the quark gluon plasma generated in heavy ion collisions. From this model the expected polarization of particles after such a collision is computed and compared to experimental data. Finally, we use the fluid gravity correspondence and a five dimensional gravitational toy model to exemplify how the new spin related transport coefficients of a strongly interactive quantum field theory can be computed from a dual gravitational theory.