We integrate numerically axially symmetric stationary Einstein equations describing self-gravitating disks around spinless black holes. The numerical scheme is based on a method developed by Shibata, but contains important new ingredients. We derive a new general-relativistic Keplerian rotation law for self-gravitating disks around spinning black holes. Former results concerning rotation around spinless black holes emerge in the limit of a vanishing spin parameter. These rotation curves might be used for the description of rotating stars, after appropriate modification around the symmetry axis. They can be applied to the description of compact torus–black hole configurations, including active galactic nuclei or products of coalescences of two neutron stars.

• Received 8 February 2018

DOI:https://doi.org/10.1103/PhysRevD.97.104017