Entropy of Black Holes in D=5, N=2 Supergravity and AdS Central Charges

TL;DR

This paper investigates black hole entropy in five-dimensional N=2 supergravity, using duality transformations and AdS/CFT correspondence to accurately count microstates and reconcile previous discrepancies in entropy calculations.

Contribution

It introduces a duality transformation linking black holes to black strings, enabling microstate counting via AdS_3 geometry, and resolves prior entropy calculation issues.

Findings

Microstate counting matches Bekenstein-Hawking entropy in AdS_3

Duality transformation connects black holes to black strings

Resolves previous discrepancies in entropy calculations

Abstract

We consider general black holes in D=5, N=2 supergravity coupled to vector multiplets, and discuss the issue of microstate counting from various viewpoints. The statistical entropy is computed for the near-extremal case using the central charge of the $AdS_2$ factor appearing in the near-horizon geometry. Furthermore, we explicitly construct the duality transformation connecting electrically charged black holes to magnetically charged black strings, under which the $AdS_2 \times S^3$ near horizon geometry becomes $AdS_3 \times S^2$. For $AdS_3$ the counting of microstates correctly reproduces the Bekenstein-Hawking entropy, thus resolving the discrepancy previously found for $AdS_2$.