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

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 $Ad{S}_2$ 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 $Ad{S}_2\times S^3$ near horizon geometry becomes $Ad{S}_3\times S^2$. For $Ad{S}_3$ the counting of microstates correctly reproduces the Bekenstein-Hawking entropy, thus resolving the discrepancy previously found for $Ad{S}_2$.

25 pages, Latex, no figures, references added