General-relativistic versus Newtonian: Geometric dragging and dynamic antidragging in stationary self-gravitating disks in the first post-Newtonian approximation

We evaluate general-relativistic effects in the motion of stationary self-gravitating accretion disks around a Schwarzschild black hole, assuming the first post-Newtonian (1PN) approximation. There arises an integrability condition that leads to the emergence of two types of general-relativistic corrections to a Newtonian rotation curve. The well-known geometric dragging of frames accelerates rotation, but the hitherto unknown dynamic term, that reflects the disk structure, decelerates rotation. The net result can diminish the Newtonian angular velocity of rotation in a central disk zone, but the geometric dragging of frames dominates in the disk boundary zone. Both effects are nonlinear in nature, and they disappear in the limit of test fluids. Dust disks can only be geometrically dragged, while uniformly rotating gaseous disks are untouched at the 1PN order. General-relativistic contributions can strongly affect rotation periods in Keplerian motion for compact systems.