Accretion disks around black holes
The physics of accretion flow very close to a black hole is dominated by several general relativistic effects. It cannot be described by the standard Shakura Sunyaev model or by its relativistic version developed by Novikov and Thome. The most important of these effects is a dynamical mass loss from the inner edge of the disk (Roche lobe overflow). The relativistic Roche lobe overflow induces a strong advective cooling, which is sufficient to stabilize local, axially symmetric thermal and viscous modes. It also stabilizes the non-axially-symmetric global modes discovered by Papaloizou and Pringle. The Roche lobe overflow, however, destabilizes sufficiently self-gravitating accretion disks with respect to a catastrophic runaway of mass due to minute changes of the gravitational field induced by the changes in the mass and angular momentum of the central black hole. One of the two acoustic modes may become trapped near the inner edge of the disk. All these effects, absent in the standard model, have dramatic implications for time-dependent behavior of the accretion disks around black holes.