Duality and Four-Dimensional Black Holes

Abstract

We consider the effects of abelian duality transformations on static, spherically-symmetric, asymptotically flat string spacetimes in four dimensions, where the dilaton, axion, metric, and gauge fields are allowed to be nonzero. Independent of the alpha' expansion, there is a six-parameter family of such configurations, labelled by the charges characterizing the asymptotic behaviour of the various fields: ie their mass, dilaton charge, axion charge, electric charge, magnetic charge, and Taub-NUT parameter. We show that duality, based on time-translation invariance, maps these solutions amongst themselves, with the effect of interchanging two pairs of these six labels, namely: (1) the mass and dilaton charge, and (2) the axion charge and the Taub-NUT parameter. We consider in detail the special case of the purely Schwarzschild black hole, for which the mass of the dual configuration vanishes to leading order in alpha'. Working to next-to-leading order in alpha' for the bosonic and heterotic strings, we find that duality takes a black hole of mass M to a (singular) solution having mass - 1/(alpha' M). Finally, we argue that two solutions which are related by duality based on a noncompact symmetry are {\it not} always physically equivalent.

plain TeX, 37 pages, no figures. We have made some minor improvements in presentation and have included some additional references

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• Regular S-Brane Backgrounds
• Yoga Dark Energy: Natural Relaxation and Other Dark Implications of a Supersymmetric Gravity Sector
• Duality and Global Symmetries
• Naked singularities in low energy, effective string theory
• Two and three loop alpha' corrections to T-duality: Kasner and Schwarzschild
• On Some New Black String Solutions in Three Dimensions
• Quadratic alpha' corrections to T-duality
• Gravitational Forces on a Codimension-2 Brane
• Symmetries of Four-dimensional String Effective Action with Cosmological Constant