General static spherically symmetric black holes of the heterotic string on a six-torus

DOI10.1016/0550-3213(96)00219-2zbMATH Open1003.83514arXivhep-th/9512127OpenAlexW1978853723MaRDI QIDQ1921052

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Publication date: 12 August 1996

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Abstract: We present the most general static, spherically symmetric solutions of 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 $SO(1,1)subsetO(8,24)$ 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 {it 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 $[SO(6)imesSO(22)]/[SO(4)imesSO(20)]subsetO(6,22)$ (T-duality) transformation and $SO(2)subsetSL(2,R)$ (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 Schwarzschild or Reissner-Nordstr" om black hole, while extreme ones have either null (or naked) singularity, or the space-time of extreme Reissner-Nordstr" om black hole.

Full work available at URL: https://arxiv.org/abs/hep-th/9512127

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