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

• 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 insulators. 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 in 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. 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.
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Jing-Bo Wang. Microscopic states of Kerr black holes from boundary-bulk correspondence[J]. Chinese Physics C.
Jing-Bo Wang. Microscopic states of Kerr black holes from boundary-bulk correspondence[J]. Chinese Physics C.
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## Microscopic states of Kerr black holes from boundary-bulk correspondence

• Institute for Gravitation and Astrophysics, College of Physics and Electronic Engineering, Xinyang Normal University, Xinyang, 464000, P. R. China

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 insulators. 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 in 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. 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.

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