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.
Highlights
Black hole entropy has some surprisingly universal properties that are accessible through semi-classical considerations
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
Since the calculations involved in deriving (1.1) and (1.2) require only theories and methods that have been tested to high accuracy experimentally, namely general relativity (GR) and perturbative quantum field theory, these formulas are the closest template to a positive experimental result we have for gravity beyond classical GR.1
Summary
Black hole entropy has some surprisingly universal properties that are accessible through semi-classical considerations. While (1.3) was derived through analysis at the classical level, its Cardy-like form suggests a simple dual field theoretical interpretation This provides a first hint that (semi-)classical considerations phrased in a ‘near horizon picture’ (we shall be more precise below what we mean by this notion) may provide insights into black hole microstates. For four-dimensional asymptotically flat solutions to Einstein gravity, it was noted that there are diffeomorphic geometries which differ by their boundary behavior and that the conserved charges associated with the diffeomorphisms relating these geometries form an infinite dimensional algebra — the asymptotic symmetry algebra — known as BMS4 algebra [28, 29]. The analysis was extended for all nonextremal black holes in the class of Banados geometries [51] in [2], where it was shown that the resulting entropy, as expected, is an invariant of Virasoro coajoint orbits
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