Potential flows in the Reissner-Nordstr\"om-(anti) de Sitter metric: numerical results

Numerical solutions for the integral curves of the velocity field (streamlines), the density contours, and the accretion rate of a steady-state flow of an ideal fluid with $p=K n^\gamma$ equation of state are presented. The streamlines and velocity fields associated with a black hole and a rigid sphere in a Reissner-Nordstr\"om-(anti) de Sitter spacetimes are studied in some detail. For each case the fluid density is studied using contour lines. For $\gamma \neq 2$, we found that the studied properties of the fluid are more sensitive to variations of the electric charge and the cosmological constant. Also, the accretion rate was found to increase or decrease when the cosmological constant increases or decreases respectively.