State space of a black hole and soft hair

In this article, we reflect on a problem of a black hole entropy. The main point of the article is that the black hole horizon should be treated as a boundary as well as the boundary at infinity. To make things more concrete, we apply the general ideas to the extremal Oliva-Tempo-Troncoso black hole and construct the corresponding Hilbert space using near-horizon hair. After creating the state space by using the proposed construction, we identify the natural candidates for the microstates responsible for the black hole entropy. The correct value of the black hole entropy is reproduced by counting the number of distinct microstates and applying the Boltzmann formula.