Statistical interpretation of Bekenstein entropy for systems with a stretched horizon

TL;DR

The paper investigates whether the Bekenstein entropy for 2-charge extremal holes in string theory can be interpreted as a coarse-graining entropy over microstate geometries. By mapping FP string states to D1-D5 bound-state geometries and introducing a stretched horizon at r ~ b where distinct microstate geometries diverge, the authors show that the Bekenstein entropy computed from the stretched-horizon area matches the microstate count. This provides a geometric interpretation of black-hole entropy as counting distinct microstate geometries and holds across duality-related 2-charge systems. The work highlights the role of the throat end structure and microstate hair, and frames the stretched horizon as a natural coarse-graining surface encoding information about microstate diversity.

Abstract

For the 2-charge extremal holes in string theory we show that the Bekenstein entropy obtained from the area of the stretched horizon has a statistical interpretation as a `coarse graining entropy': different microstates give geometries that differ near r=0 and the stretched horizon cuts off the metric at r=b where these geometries start to differ.

Figures (3)

• Figure 1: (a) the geometry for $r\gg b$; (b) two different possible ends to the throat; (c) truncation by a stretched horizon.
• Figure 2: A typical singular curve (dashed line) and stretched horizon (torus surface) for $J\gg \sqrt{n_1n_5}$.
• Figure 3: Typical geodesic (dashed line) near the singular curve (solid line).