Basic properties of toroidal structures in Kerr--de Sitter backgrounds

Perfect fluid tori with uniform distribution of the specific angular momentum orbiting the Kerr-de Sitter black holes or naked singularities are studied. Closed equipotential surfaces corresponding to stationary toroidal discs are allowed only in the spacetimes admitting stable circular geodesics. The last closed surface crosses itself in the cusp(s) enabling outflow(s) of matter from the torus due to the violation of hydrostatic equilibrium. The repulsive cosmological constant, $\Lambda >0$, implies the existence of the outer cusp (with a stabilizing effect on the tori because of "excretion", i.e., outflow of matter from the torus into the outer space) and the strong collimation of open equipotential surfaces along the rotational axis. Both the effects take place nearby the so-called static radius where the gravitational attraction is just balanced by the cosmic repulsion. The plus-family discs (which are always corotating in the black-hole backgrounds but can be counterrotating, even with negative energy of the fluid elements, in some naked singularity backgrounds) are thicker and more extended than the minus-family ones (which are always counterrotating in all backgrounds). If the parameters of naked-singularity spacetimes are very close to the parameters of extreme black-hole spacetimes, the family of possible disc-like configurations includes members with two isolated discs where the inner one is always a counterrotating accretion disc. Mass estimates for tori with nonrelativistic adiabatic equation of state give limits on their central mass-density, for which the approximation of test fluid is adequate.