Disk-Accretion onto a Black Hole. II. Evolution of the Hole

When a black hole swallows matter and radiation from an accretion disk, its mass M and angular momentum J Ma change-i.e., the hole evolves. The details of that evolution are calculated. The accreting matter, by itself, would spin the hole up to a = M ("extreme-Kerr hole") after a modest amount of accretion ( M/M 1.5). However, the radiation emitted by the disk and swallowed by the hole produces a counteracting torque, which prevents spin-up beyond a limiting state of (aIM)11 0.998. This limiting state corresponds to a maximum efficiency of 30 percent for the hole's conversion of accreting mass into outgoing photon energy. In IV it is argued that realistic phenomena ignored in this calculation (magnetic fields dragged down the hole by accreting matter; heating of outer parts of disk by X-rays from inner parts... .) might not change significantly the values (aIM)11 0.998 and (maximum efficiency) 0.30. Subject headings: black holes - rotation