tokens: to evolve only a slice spanning ( r , θ), and with constant φ, thus assuming that the system will remain rotationally symmetric during the evolution. In order to justify to what extent and under which conditions this assumption is valid the comparison with 3D computation was needed. We will comment on that in Section 4.3 . However, within the 2.5-D approach, the φ component of the four-velocity is considered. We prescribe this component in Boyer–Lindquist coordinates according to relations given by equations ( 4 ) and ( 5 ). We chose several exemplary simulations and show their results in the form of snapshots. Every snapshot contains four panels with the slices of and its equatorial profile, ρ in arbitrary units, and λ in geometrized units, and it is labelled by the time t in geometrized units, where M is the mass of central black hole. The axes show the position in geometrized units. The red colour in the slice of radial Mach number corresponds to the supersonic motion, and blue regions indicate the subsonic accretion. The shock front is located at the place where the abrupt change from supersonic to subsonic motion occurs, hence it is represented with the white curve separating red region farther from the centre and blue region closer to the centre. The sonic curves are also white, but they lie between the blue region farther and red region closer to the centre. On top of the radial Mach number map the velocity streamlines are plotted in blue. These streamlines are computed from the velocity field at the given instant of time, hence they do not represent the actual history of a certain fluid parcel. 4.2.1 Bondi solution equipped with angular momentum At the beginning we check that for pure Bondi solution with λ = 0 we get the stationary solution of the flow with the properties consistent with the analytical solution. After that, we start to study the slowly rotating flows. For the first simulation, we pick the parameters such that λ eq belongs to the multicritical region (the region in the parameter space where both the inner and outer sonic points exist in the 1D model), but it is very close to its upper bound, in particular , λ eq = 3.6M and γ = 4/3. In that case, even when the shock solution is possible, it is not expected to appear, because the initial configuration is closer to the outer branch (there is no inner sonic point in the Bondi initial data.). In other words, we expect that the rotation of the gas affects the profile of the Mach number in the innermost region in such a way that it gets very close to 1, but does not touch it. In Fig. 2 , the initial conditions at t = 0 M are shown and the final state at t f = 10 4 M of the gas is depicted in Fig. 7 . At the later time, the simulation is already relaxed to the stationary state, which resembles the outer branch. It is interesting to note that for t = t f the Mach number actually crosses the line, however only on a very short radial range. Usually, the presence of the
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