Aspects of black hole entropy

There have been many attempts to understand the statistical origin of black-hole entropy. Among them, entanglement entropy and the brick wall model are strong candidates. In this paper, first, we show that the entanglement approach reduces to the brick wall model when we seek the maximal entanglement entropy. After that, 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 brick wall model is well defined even in a rotating background if the inner boundary is sufficiently close to the horizon. These results strongly suggest that the entanglement approach is also well defined in a rotating background.