  We investigate models of stationary, selfgravitating, perfect-fluid tori
(disks) rotating around black holes, focusing on geometric properties of
spacetime. The models are constructed within the general-relativistic
hydrodynamics, assuming differential (Keplerian) rotation of the fluid. We
discuss a parametric bifurcation occurring in the solution space, different
possible configurations of ergoregions (including toroidal ergoregions
associated with the tori), nonmonotonicity of the circumferential radius, as
well as the impact of the torus gravity on the location of the innermost stable
circular orbit.
