Quantization of horizon areas of the Kerr black hole

TL;DR

This paper proposes a new approach to quantize Kerr black hole horizons by incorporating three types of resonance modes, leading to equally spaced inner and outer horizon areas consistent with Bekenstein's proposal.

Contribution

It introduces the use of quasinormal, total transmission, and total reflection modes collectively to derive the quantized horizon areas of Kerr black holes.

Findings

Inner and outer horizon areas are equally spaced.

The approach is applicable to Reissner-Nordstrom black holes.

All resonance modes depend only on black hole parameters.

Abstract

Since the Bekenstein's proposal that a black hole has equally spaced area spectrum, the quasinormal modes as the characteristic modes of a black hole have been used in obtaining the horizon area spectrum of the black hole. However, the area spectrum of the Kerr black hole in some previous works was inconsistent with the Bekenstein's proposal. In this paper, we notice that the Kerr black hole has three types of resonance modes which are quasinormal modes (QNM), total transmission modes (TTM), and total reflection modes (TRM). All of these resonances represent highly damped oscillations and only depend on the black hole parameters which are mass, charge and angular momentum of the black hole. We propose that all of these modes should be used in quantizing the black hole. With all these modes, we find that both the inner and outer horizon areas of the Kerr black hole are equally spaced. Similar behavior is also found in the Reissner-Nordstrom black hole.