  An open system consisting of a scalar field bound to a Kerr black hole whose
mass ($M$) and specific angular momentum ($a$) are slowly (adiabatically)
perturbed is considered. The adiabatically induced phase and the conditions for
the validity of the adiabatic approximation are obtained. The effect of closed
cycles in parameter space ($a$, $M$ plane) on the energy levels of both stable
and unstable scalar field bound states, together with other quantities of
interest, is illustrated. Lastly it is noted that the black hole wavefunction
will acquire an equal and opposite phase to that of matter thus leading to a
change of its effective action (entropy).
