How Are Black Holes Quantized?

TL;DR

This paper reviews various methods for quantizing black hole horizons, showing that maximum entropy scales with surface area in the classical limit, but highlights unresolved issues for rotating black holes.

Contribution

It demonstrates the proportionality of maximum entropy to surface area across multiple quantization approaches and discusses the open problem of rotating black hole quantization.

Findings

Maximum entropy proportional to surface area in classical limit

General class of surface quantization approaches analyzed

No satisfactory quantization solution for rotating black holes yet

Abstract

Some approaches to quantization of the horizon area of black holes are discussed. The maximum entropy of a quantized surface is demonstrated to be proportional to the surface area in the classical limit. This result is valid for a rather general class of approaches to surface quantization. In the case of rotating black holes no satisfactory solution for the quantization problem has been found up to now.