Is the brick-wall model unstable for a rotating background? art. no. 124021

The stability of the brick-wall model is analyzed in a rotating background. It is shown that, in the Kerr background without an horizon but with an in ner boundary, a scalar field has complex-frequency modes and that, however, the imaginary part of the complex frequency can be small enough compared w ith 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. Si nce ambient fields should settle in the thermal state in the latter time sc ale, the instability is not so catastrophic. Thus the brick-wall model is w ell defined even in a rotating background if the inner boundary is sufficie ntly close to the horizon.