General static spherically symmetric black holes of the heterotic string on a six-torus
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We present the most general static, spherically symmetric solutions of the heterotic string compactified on a six-torus that conforms to the conjectured “no-hair theorem”, by performing a subset of O(8,24) transformations, i.e. symmetry transformations of the effective three-dimensional action for stationary solutions, on the Schwarzschild solution. The explicit form of the generating solution is determined by six SO(1,1) 
O(8,24) boosts, with the zero Taub-NUT charge constraint imposing one constraint among two boost parameters. The non-nontrivial scalar fields are the axion-dilaton field and the moduli of the two-torus. The general solution, parameterized by unconstrained 28 magnetic and 28 electric charges and the ADM mass compatible with the Bogomol'nyi bound, is obtained by imposing on the generating solution O(6,22) (T-duality) transformation and SO(2) SL (2,R) (S-duality) transformation, which do not affect the four-dimensional space-time. Depending on the range of boost parameters, the non-extreme solutions have the space-time of either the Schwarzschild or the Reissner-Nordström black hole, while the extreme ones have either a null (or naked) singularity, or the space-time of the extreme Reissner-Nordström black hole.
O(8,24) boosts, with the zero Taub-NUT charge constraint imposing one constraint among two boost parameters. The non-nontrivial scalar fields are the axion-dilaton field and the moduli of the two-torus. The general solution, parameterized by unconstrained 28 magnetic and 28 electric charges and the ADM mass compatible with the Bogomol'nyi bound, is obtained by imposing on the generating solution O(6,22) (T-duality) transformation and SO(2) SL (2,R) (S-duality) transformation, which do not affect the four-dimensional space-time. Depending on the range of boost parameters, the non-extreme solutions have the space-time of either the Schwarzschild or the Reissner-Nordström black hole, while the extreme ones have either a null (or naked) singularity, or the space-time of the extreme Reissner-Nordström black hole.