infalling matter is greater than unity and under these conditions, the luminosity approaches the Eddington limit (Milosavljevic et al. 2009). However, some authors claim that super-Eddington luminosities are possible if the black-hole is embedded in a very dense gas that decreases the importance of radiation pressure effects (Pacucci et al. 2015). Super-Eddington accretion rates were also found in some radiation-hydrodynamics simulations but based on one-dimensional geometry and particular conditions of the ambient gas (Inayoshi et al. 2016). However, it is not certain whether such extreme conditions are sustainable considering the violent environments of the first galaxies where the medium is affected by the star formation activity and supernovae.

If the BH is moving with respect to the gas, the situation is rather different. After passing the BH, a conically shaped shock is produced in the flow in which the gas loses the momentum component perpendicular to the shock front. After compression in the shock, gas particles within a certain impact parameter will fall into the BH. One determinant factor describing the subsequent motion of the gas is the angular momentum. If the infalling gas has an specific angular momentum $J$ that exceeds $2r_gc$, where $r_g = 2GM/c^2$ is the gravitational 