General relativistic hydrodynamic flows around a static compact object in final stages of accretion flow

Dynamics of stationary axisymmetric configuration of the viscous accreting fluids surrounding a non-rotating compact object in final stages of accretion flow is presented here. For the special case of thin disk approximation, the relativistic fluid equations ignoring self-gravity of the disk are derived in Schwarzschild geometry. For two different state equations, two sets of self-consistent analytical solutions of fully relativistic fluid equations are obtained separately. The effect of bulk viscosity coefficient on the physical functions are investigated for each state equation, as well as the bounds that exert on the free parameters due to the condition of accretion flow in the last stages. The solutions found show that the radial and azimuthal velocities, density and pressure of the fluid increase inwards for both state equations. Also, viscosity has no effect on the velocities and density distributions in both state equations. Two state equations show different types of behavior with respect to the bulk viscosity coefficient. For p=K state equation, if there is no bulk viscosity, the pressure remains constant throughout the disk, whereas with increasing bulk viscosity the pressure falls off in the inner regions but soon stabilizes at an almost constant value. However, for p=ρc2 state equation, the pressure is never constant, even in the absence of bulk viscosity. The larger the value of ηb, the higher the value of pressure in the inner regions.