General Relativistic theory of viscous accretion disks around Black Holes

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In this project we will study the relativistic theory of accretion disks around Black Holes. With their innermost stable circular orbits accretion disks can approach Black Holes very closely. Thus, accretion disks are a perfect probe of the strong gravity regime. We will model accretion disks by relativistic fluids with viscosity in the external geometry of a Black Hole. For that we first will derive the equations of motion for the accretion disks with two complementary methods: (i) from the phenomenological gradient expansion scheme and (ii) from the general relativistic kinetic theory. For the resulting effective relativistic hydrodynamical or fluid theoretical equations of motion we expect additional couplings to space-time curvature which are beyond the minimal coupling of the special relativistic hydrodynamical equations and which may have some influence on the accretion disk near to steller Black Holes. Using this equation of motion we then will investigate (a) the form and structure of the accretion disks, (b) the physics of the innermost stable circular orbits, (c) the oscillatory dynamics of accretion disks, and (d) the accretion rate, and other observable properties. The results of the calculations will be compared with available observations. Since we also will explore and test the strong gravity regime we will not only assume the Kerr space-time as external space-time geometry, but apply the formalism also to more general Black Hole space-times and also to Black Hole solutions of generalized theories of gravity.