Microscopic derivation of the Bekenstein-Hawking entropy formula for non-extremal black holes

TL;DR

The paper provides a microscopic derivation of the Bekenstein--Hawking entropy for non-extremal, non-supersymmetric 4d/5d black holes by mapping them through U-duality to BTZ-containing configurations and counting horizon degrees of freedom via Carlip's boundary conformal field theory. It shows that the horizon area—and thus the entropy $S_{BH} = \frac{A}{4 G_N^{(d)}}$—is preserved under these dualities, allowing a 3d BTZ-based microstate count to reproduce the correct coefficient. The work also connects these results to D-brane pictures via AdS supersingleton representations and discusses extensions to higher dimensions, where BTZ is not present and AdS$_{4,5,7}$ boundary theories would govern the microstates. Overall, the approach unifies non-extremal black hole entropy with AdS/CFT-inspired boundary dynamics and clarifies the role of dualities and singleton degrees of freedom in black hole thermodynamics.

Abstract

We derive the Bekenstein-Hawking entropy formula for four and five dimensional non-supersymmetric black holes (which include the Schwarzchild ones) by counting microscopic states. This is achieved by first showing that these black holes are U-dual to the three-dimensional black hole of Banados-Teitelboim-Zanelli and then counting microscopic states of the latter following Carlip's approach. Higher than five dimensional black holes are also considered. We discuss the connection of our approach to the D-brane picture.