Phase space mixing in the equatorial plane of a Kerr black hole
  It is shown that a collisionless, relativistic kinetic gas configuration
propagating in the equatorial plane of a Kerr black hole undergoes a relaxation
process and eventually settles down to a stationary, axisymmetric configuration
surrounding the black hole. The underlying mechanism for this relaxation
process is due to phase space mixing, which implies that although the
one-particle distribution function $f$ satisfying the collisionless Boltzmann
equation which describes the microscopic state of the gas is quasi-periodic in
time, the associated macroscopic observables computed from averages over $f$
possess well-defined limits as time goes to infinity. The final state of the
gas is described by an effective distribution function depending only on
constants of motion which can be predicted from the initial distribution
function.
