Pseudo-Newtonian and general relativistic barotropic tori in Schwarzschild-de Sitter spacetimes

Pseudo-Newtonian gravitational potential introduced in spherically symmetric black-hole spacetimes with a repulsive cosmological constant is tested for equilibrium toroidal configurations of barotropic perfect fluid orbiting the black holes. Shapes and potential depths are determined for the marginally stable barotropic tori with uniform distribution of specific angular momentum, using both the pseudo-Newtonian and fully relativistic approach. For the adiabatic (isoentropic) perfect fluid, temperature profiles, mass-density and pressure profiles and total masses of pseudo-Newtonian and relativistic tori are compared providing important information on the relevance of the test-disc approximation in both the approaches. It is shown that the pseudo-Newtonian approach can be precise enough and useful for the modelling of accretion discs in the Schwarzschild-de Sitter spacetimes with the cosmological parameter y = ΛM2/3 ∼< 10-6. For astrophysically relevant black holes with y < 10-25, this statement is tested and shown to be precise in few per cent for both accretion and excretion tori and for the marginally bound, i.e. maximally extended, tori allowing simultaneous inflow to the black hole and outflow to the outer space.