Duality and four-dimensional black holes
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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.