Entropy Enhancement and Black Hole Microstates

TL;DR

This work shows that black-hole entropy may originate from horizonless microstate geometries populated by fluctuating two-charge supertubes in three-charge backgrounds. Through a Born-Infeld probe analysis on a Gibbons-Hawking base, the authors demonstrate that the tube entropy is governed by locally enhanced effective charges $Q_I^{eff}$ rather than asymptotic charges, and that deep scaling throats with strong magnetic flux can dramatically boost these charges. Cardy counting applied to the tube fluctuations yields $S = 2\pi\sqrt{ Q_{1}^{eff} Q_{3}^{eff} - n_2^{2} Z_2 / V }$, illustrating how entropy can become macroscopic when $Q_I^{eff}$ are large. They provide concrete scaling solutions and an explicit Taub-NUT example showing $Q_I^{eff}$ can scale like $\lambda^{-1}$ as the throat deepens, supporting the possibility that smooth, horizonless configurations can account for black-hole-like entropy in the regime where classical black holes exist. The work outlines a path to realising black-hole entropy within horizonless microstates, while highlighting the need for fully back-reacted solutions to confirm the mechanism and its universality.

Abstract

We study fluctuating two-charge supertubes in three-charge geometries. We show that the entropy of these supertubes is determined by their locally-defined effective charges, which differ from their asymptotic charges by terms proportional to the background magnetic fields. When supertubes are placed in deep, scaling microstate solutions, these effective charges can become very large, leading to a much larger entropy than one naively would expect. Since fluctuating supertubes source smooth geometries in certain duality frames, we propose that such an entropy enhancement mechanism might lead to a black-hole like entropy coming entirely from configurations that are smooth and horizonless in the regime of parameters where the classical black hole exists.