  The present paper is a follow-up of our previous paper that derives a
slightly simplified model equation for the Klein-Gordon equation, describing
the propagation of a scalar field of mass $\mu$ in the background of a rotating
black hole and, among others, supports the instability of the field down to
$a/M \approx 0.97$. The latter result was derived numerically. This paper gives
corresponding rigorous results, supporting instability of the field down to
$a/M \approx 0.979796$.
