Statistical Description of Rotating Kaluza-Klein Black Holes

TL;DR

This paper extends the microscopic D-brane description of extremal Kaluza-Klein black holes to fast rotation, where ergospheres and nonzero horizon angular velocity appear, drawing close parallels to Kerr black holes. By mapping rotating KK black holes to D0-D6 brane systems and to intersecting D3-branes, the authors show that the entropy is reproduced exactly in both slow and fast rotation regimes, while the mass undergoes renormalization at strong coupling in the fast regime. They analyze ergospheres and superradiance from the microscopic perspective, and connect 4D KK solutions to 5D Myers-Perry limits, illuminating how horizon geometry and near-horizon symmetries govern thermodynamic quantities. The work supports attractor-based arguments for universality of entropy and highlights when microscopic descriptions fix mass versus when they renormalize, with implications for understanding extremal Kerr-like black holes. Overall, the results offer a coherent microscopic account of rotating KK black holes and their relation to broader AdS/CFT structures.

Abstract

We extend the recent microscopic analysis of extremal dyonic Kaluza-Klein (D0-D6) black holes to cover the regime of fast rotation in addition to slow rotation. Fastly rotating black holes, in contrast to slow ones, have non-zero angular velocity and possess ergospheres, so they are more similar to the Kerr black hole. The D-brane model reproduces their entropy exactly, but the mass gets renormalized from weak to strong coupling, in agreement with recent macroscopic analyses of rotating attractors. We discuss how the existence of the ergosphere and superradiance manifest themselves within the microscopic model. In addition, we show in full generality how Myers-Perry black holes are obtained as a limit of Kaluza-Klein black holes, and discuss the slow and fast rotation regimes and superradiance in this context.