Is the brick-wall model unstable for a rotating background?

TL;DR

This paper investigates the stability of the brick wall model in a rotating Kerr background, finding that it remains stable if the inner boundary is close enough to the horizon, making the model viable in such scenarios.

Contribution

It demonstrates that the brick wall model is stable in a rotating background when the inner boundary is near the horizon, addressing previous concerns about instability.

Findings

Complex-frequency modes exist in the Kerr background without horizon.

The imaginary part of the frequency can be small if the boundary is close to the horizon.

The instability time scale is much longer than the thermal relaxation time.

Abstract

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.