Near Horizon Geometry of Rotating Black Holes in Five Dimensions

TL;DR

The paper shows that general rotating five-dimensional black holes can be understood as rotating six-dimensional strings with near-horizon geometry locally given by $AdS_3\times S^3$. The decoupling limit yields a BTZ black hole times $S^3$, enabling a boundary CFT with central charge $c$ to count microstates via Cardy’s formula, reproducing the macroscopic entropy while encoding rotation. Perturbations in this background organize into $SL(2,\mathbb{R})_L\times SL(2,\mathbb{R})_R$ multiplets, and greybody factors connect the spectrum to the effective D1–D5 string description. The results strengthen the AdS/CFT perspective on black hole microphysics, clarifying how rotation modifies the near-horizon CFT and the associated perturbation structure, and linking spacetime physics to the D1–D5 worldsheet theory.

Abstract

We interpret the general rotating black holes in five dimensions as rotating black strings in six dimensions. In the near horizon limit the geometry is locally AdS_3 x S_3, as in the nonrotating case. However, the global structure couples the AdS_3 and the S_3, giving angular velocity to the S_3. The asymptotic geometry is exploited to count the microstates and recover the precise value of the Bekenstein- Hawking entropy, with rotation taken properly into account. We discuss the perturbation spectrum of the rotating black hole, and its relation to the underlying conformal field theory.