W-hairs of black holes in three dimensional spacetime

In the previous paper (arXiv:1804.09438) we found that the near horizon symmetry algebra of black holes is a subalgebra of the $W_{1+\mathrm{\infty }}$ 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 $W_{1+\mathrm{\infty }}$ algebra, we count the number of the microstates of the BTZ black holes and obtain the Bekenstein-Hawking entropy.