Supersymmetric rotating black holes and attractors

Five-dimensional stringy rotating black holes are embedded into $N=2\mathrm{}$ 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 supercurvature. The area of the horizon of the rotating supersymmetric black holes is found to be $\sqrt{Z_{\mathrm{fix}}^3-J^2}$, where $Z_{\mathrm{fix}}$ is the extremal value of the central charge in moduli space.