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We consider stationary, axially symmetric toroids rotating around spinlessblack holes, assuming the general-relativistic Keplerian rotation law, in thefirst post-Newtonian approximation. Numerical investigation shows that theangular momentum accumulates almost exclusively within toroids. It appears thatvarious types of dragging (anti-dragging) effects are positively correlatedwith the ratio $M_\mathrm{D}/m$ ($M_\mathrm{D}$ is the mass of a toroid and $m$is the mass of the black hole) - moreover, their maxima are proportional to$M_\mathrm{D}/m$. The horizontal sizes of investigated toroids range from c. 50to c. 450 of Schwarzschild radii $R_\mathrm{S}$ of the central black hole;their mass $M_\mathrm{D} \in (10^{-4}m, 40m)$ and the radial size of the systemis c. 500 $R_\mathrm{S}$. We found that the relative strength of variousdragging (anti-dragging) effects does not change with the mass ratio, but itdepends on the size of toroids. Several isoperimetric inequalities involvingangular momentum are shown to hold true.

Rotating systems, universal features in dragging and anti-dragging effects, and bounds onto angular momentum