W-hairs of the black holes in three-dimensional spacetime *

Abstract

Abstract In a previous publication, we claimed that a black hole can be considered as a topological insulator. A direct consequence of this claim is that their symmetries should be related. In this paper, we give a representation of the near-horizon symmetry algebra of the BTZ black hole using the W 1+∞ symmetry algebra of the topological insulator in three-dimensional spacetime. Based on the W 1+∞ algebra, we count the number of the microstates of the BTZ black holes and obtain the Bekenstein-Hawking entropy.