Supersymmetric Rotating Black Holes and Attractors

TL;DR

The paper addresses constructing supersymmetric rotating black holes in five dimensions within N=2 supergravity coupled to a vector multiplet. It shows that the BMPV-like rotating solution preserves half of the supersymmetry via Killing spinors and exhibits horizon supersymmetry enhancement despite rotation. Using very special geometry, it identifies a fixed point in moduli space (extremization of the central charge) and derives a generalized horizon area formula $A=\frac{\pi^2}{3}\sqrt{Z_{\rm fix}^{3}-J^{2}}$, connecting rotation to the attractor mechanism. These results extend attractor logic to rotating black holes and illuminate the microphysical structure of their entropy in 5D supergravity.

Abstract

Five-dimensional stringy rotating black holes are embedded into N=2 supergravity interacting with one vector multiplet. The existence of an unbroken supersymmetry of the rotating solution is proved directly by solving the Killing spinor equations. The asymptotic enhancement of supersymmetry near the horizon in the presence of rotation is established via the calculation of the super-curvature. The area of the horizon of the rotating supersymmetric black holes is found to be $\sqrt {Z_{fix}^{3 }- J^2}$, where $Z_{fix}$ is the extremal value of the central charge in moduli space.