# Microscopic states of Kerr black holes from boundary-bulk correspondence

## TL;DR

This paper explores the boundary modes of Kerr black holes using topological insulator methods, deriving new thermodynamic properties, associating a dual CFT, and confirming the Bekenstein-Hawking entropy law.

## Contribution

It extends boundary mode analysis from BTZ to Kerr black holes, introduces temperature definitions, and links microstates to a dual CFT with a specific central charge.

## Key findings

- Defined dimensionless right- and left-temperatures with consistent behavior
- Associated a central charge c=12 M r_+ for Kerr black holes
- Counted microstates matching the Bekenstein-Hawking entropy

## Abstract

It was claimed by the author that black holes can be considered as topological insulators. They both have boundary modes and those boundary modes can be described by an effective BF theory. In this paper, we analyze the boundary modes on the horizon of black holes with the methods developed for topological insulator. Firstly the BTZ black hole is analysed, and the results are compatible with the previous works. Then we generalize those results to Kerr black holes. Some new results are obtained: dimensionless right- and left-temperature can be defined and have well behaviors both in Schwarzschild limit $a\rightarrow 0$ and extremal limit $a\rightarrow M$. Upon the Kerr/CFT correspondence, we can associate a central charge $c=12 M r_+$ with an arbitrary Kerr black hole if a dual CFT exists. We can identify the microstates of the Kerr black hole with the quantum states of this scalar field. From this identification we can count the number of microstates of the Kerr black hole and give the Bekenstein-Hawking area law for the entropy.