General rotating five-dimensional black holes of toroidally compactified heterotic string

Abstract

Abstract We present the most general rotating black hole solution of five-dimensional N = 4 super-string 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.