General Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus

Details General Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus General Static Spherically Symmetric Black Holes of Heterotic String on a Six Torus

1995-12-18

arxiv.org/abs/hep-th/9512127v2

Nucl.Phys.B472:249-267,1996

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, uses RevTeX, the revised version to appear in Nuclear Physics B (explicit O(6,22) and SL(2,R) transformations are im

Scientific paper

10.1016/0550-3213(96)00219-2

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 $SO(1,1)\subset O(8,24)$ 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 {\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 $[SO(6)\times SO(22)]/[SO(4)\times SO(20)] \subset O(6,22)$ (T-duality) transformation and $SO(2)\subset SL(2,R)$ (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 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.

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