Relativistic accretion onto compact objects

The present PhD thesis summarises results on analytical accretion models obtained during my PhD studies in 2014a 2018. I present a new ansatz for specific angular momentum-angular velocity dependence for perfect fluid in circular motion around a Kerr black hole. With this ansatz new solutions for toroidal configurations were obtained. I discuss here in detail the dynamical properties of these configurations and results of their application as initial conditions for accretion simulations with 2-D HARM code. For the case of circular motion in the NUT spacetime I present my results on characteristic circular geodesics radii in it. These results are further used for modelling perfect fluid tori with constant specific angular momentum (Polish Doughnuts). Characteristic changes in the patterns of circular motion of perfect fluid due to presence of the NUT parameter are discussed. The last part of the work presents a pre-study of accretion of spinning particles/fluids onto Kerr black holes. I discuss our results on spin-induced advance in last stable orbits and its relevance for accretion models.