  The stability of the brick wall model is analyzed in a rotating background.
It is shown that in the Kerr background without horizon but with an inner
boundary a scalar field has complex-frequency modes and that, however, the
imaginary part of the complex frequency can be small enough compared with the
Hawking temperature if the inner boundary is sufficiently close to the horizon,
say at a proper altitude of Planck scale. Hence, the time scale of the
instability due to the complex frequencies is much longer than the relaxation
time scale of the thermal state with the Hawking temperature. Since ambient
fields should settle in the thermal state in the latter time scale, the
instability is not so catastrophic. Thus, the brick wall model is well defined
even in a rotating background if the inner boundary is sufficiently close to
the horizon.
