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(Abridged) A solution is obtained for the interior structure of an unchargedrotating black hole that accretes a collisionless fluid. The solution isconformally stationary, axisymmetric, and conformally separable, possessing aconformal Killing tensor. Hyper-relativistic counter-streaming betweencollisionless ingoing and outgoing streams drives inflation at (just above) theinner horizon, followed by collapse. As ingoing and outgoing streams approachthe inner horizon, they focus into twin narrow beams directed along the ingoingand outgoing principal null directions, regardless of the initial angularmotions of the streams. The radial energy-momentum of the counter-streamingbeams gravitationally accelerates the streams even faster along the principaldirections, leading to exponential growth in the streaming density andpressure, and in the Weyl curvature and mass function. At exponentially largedensity and curvature, inflation stalls, and the spacetime collapses. As thespacetime collapses, the angular motions of the freely-falling streams grow.When the angular motion has become comparable to the radial motion, whichhappens when the conformal factor has shrunk to an exponentially tiny scale,conformal separability breaks down, and the solution fails. The condition ofconformal separability prescribes the form of the ingoing and outgoingaccretion flows incident on the inner horizon. The dominant radial part of thesolution holds provided that the densities of ingoing and outgoing streamsincident on the inner horizon are uniform, independent of latitude; that is,the accretion flow is "monopole." The sub-dominant angular part of the solutionrequires a special non-radial pattern of angular motion of streams incident onthe inner horizon. The prescribed angular pattern cannot be achieved if thecollisionless streams fall freely from outside the horizon.

The interior structure of rotating black holes 2. Uncharged black holes