Horizon fluff, semi-classical black hole microstates - Log-corrections to BTZ entropy and black hole/particle correspondence

TL;DR

This work refines the horizon-fluff program for BTZ black holes in AdS3, showing that BTZ microstates can be realized as coherent states of AdS3 particles within a conic-space Virasoro sector and linking canonical and microcanonical descriptions via a precise map. The authors establish a two-field (J and W) near-horizon/CFT dual picture and demonstrate that microstates reproduce the Bekenstein–Hawking entropy, including the correct logarithmic corrections, using semi-classical (Bohr-like) quantization of deficit angles and a replica-trick analysis. A key result is the horizon-fluff entropy S_fluff matching the BTZ microcanonical entropy and the Lifshitz-inspired cross-checks, supporting a black hole/particle correspondence that situates black holes as condensates of AdS3 particles. The framework provides a universal semi-classical mechanism for black hole microstate counting that is independent of UV completions and offers a pathway to extend to more general horizons and dynamical questions, potentially informing the information paradox and horizon thermodynamics.

Abstract

According to the horizon fluff proposal microstates of a generic black hole belong to a certain subset of near horizon soft hairs that cannot be extended beyond the near horizon region. In [1,2] it was shown how the horizon fluff proposal works for AdS3 black holes. In this work we clarify further this picture by showing that BTZ black hole microstates are in general among the coherent states in the Hilbert space associated with conic spaces or their Virasoro descendants, provided we impose a (Bohr-type) quantization condition on the angular deficit. Thus BTZ black holes may be viewed as condensates (or solitonic states) of AdS3 particles. We provide canonical and microcanonical descriptions of the statistical mechanical system associated with BTZ black holes and their microstates, and relate them. As a further non-trivial check we show the horizon fluff proposal correctly reproduces the expected logarithmic corrections to the BTZ entropy.

Figures (4)

• Figure 1: BTZ horizon without (left) and with (right) soft hair excitations
• Figure 2: Particle on AdS$_3$ (left) and a Virasoro descendant thereof (right)
• Figure 3: Hilbert spaces $\mathcal{H}_{\textrm{\tiny Vir}}$ (left) and $\mathcal{H}_{\boldsymbol{J}}$ (right)
• Figure 4: Schematic depiction of horizon fluff proposal