  The current early stage in the investigation of the stability of the Kerr
metric is characterized by the study of appropriate model problems.
Particularly interesting is the problem of the stability of the solutions of
the Klein-Gordon equation, describing the propagation of a scalar field of mass
$\mu$ in the background of a rotating black hole. Rigorous results proof the
stability of the reduced, by separation in the azimuth angle in Boyer-Lindquist
coordinates, field for sufficiently large masses. Some, but not all, numerical
investigations find instability of the reduced field for rotational parameters
$a$ extremely close to 1. Among others, the paper derives a model problem for
the equation which supports the instability of the field down to $a/M \approx
0.97$.
