W-hairs of black holes in three dimensional spacetime

TL;DR

This paper explores the algebraic structure of black hole horizons in three-dimensional spacetime, connecting near horizon symmetries to quantum Hall fluid symmetries, and uses this to count microstates and derive black hole entropy.

Contribution

It presents a new representation of the near horizon symmetry algebra related to the $W_{1+ ablafty}$ algebra, enabling microstate counting for BTZ black holes.

Findings

Derived the Bekenstein-Hawking entropy from algebraic microstate counting.

Connected black hole horizon symmetries to quantum Hall fluid algebra.

Provided a novel algebraic framework for black hole microstates.

Abstract

In the previous paper (arXiv:1804.09438) we found that the near horizon symmetry algebra of black holes is a subalgebra of the $W_{1+\infty}$ symmetry algebra of quantum Hall fluid in three dimensional spacetime. In this paper, we give a slightly different representation of the former algebra from the latter one. Similar to the horizon fluff proposal, based on the $W_{1+\infty}$ algebra, we count the number of the microstates of the BTZ black holes and obtain the Bekenstein-Hawking entropy.