General Rotating Five Dimensional Black Holes of Toroidally Compactified Heterotic String

We present the most general rotating black hole solution of five-dimensional N=4 superstring vacua that conforms to the “no hair theorem”. It is chosen to be parameterized in terms of massless fields of the toroidally compactified heterotic string. The solutions are obtained by performing a subset of O(8,24) transformations, i.e., symmetry transformations of the effective three-dimensional action for stationary solutions, on the five-dimensional (neutral) rotating solution parameterized by the mass m and two rotational parameters $l_1$ and $l_2$. The explicit form of the generating solution is determined by three $SO(1,1)⊂ O(8,24)$ boosts, which specify two electric charges $Q_1^(1), Q_2^(2)$ of the Kaluza-Klein and two-form U(1) gauge fields associated with the same compactified direction, and the charge Q (electric charge of the vector field, whose field strength is dual to the field strength of the five-dimensional two-form field). The general solution, parameterized by 27 charges, two rotational parameters and the ADM mass compatible with the Bogomol'nyi bound, is obtained by imposing $[SO(5)× SO(21)]/[SO(4)× SO(20)]⊂ O(5,21)$ transformations, which do not affect the five-dimensional space-time. We also analyze the deviations from the BPS-saturated limit.