General relativistic theory of spin-fluid accretion disks around Black Holes

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Since accretion disks can approach Black Holes very closely they are an important tool to investigate the strong gravity or the near horizon regime. The behavior of accretion disks depends on the material the disks is made of as well as on the space-time geometry. Usually accretions disks are modeled either by an ideal fluid with mass density and pressure or -- in order to account for the accretion process -- with viscosity. Also charged fluids or plasma have been discussed. Since interstellar matter -- in particular in strong gravity regions -- may consist of atoms or elementary particles it might be conceivable that also the spin or the magnetic moment of these atomic or sub-atomic constituents may play a role in the behavior of accretion disks. Accordingly, the present proposal discusses spin fluids as matter model for accretion disks. Compared with the usually assumed matter models, here additional couplings of the spin to the space-time curvature and to external electromagnetic fields of, e.g., galactic origin will be present and probably influence the physical properties of the disk. Spin also offers a preferred tool to search for a hypothetical space-time torsion. Beside that, spin fluids also ask for dedicated studies of the hyperbolicity of the equations of motion and, consequently, of causality. A further aspect is the need to implement supplementary spin conditions which may influence the equations of motion and, thus, also the hyperbolicity. These properties may also depend on the existence of a hypothetical torsion. The final aim of this project then is to calculate the physical properties of accretion disk, that is, its shape, the density profile, oscillations, and other characteristics.