  It has been argued by Dyson in the context of QED in flat spacetime that
perturbative expansions in powers of the electric charge e cannot be convergent
because if e is purely imaginary then the vacuum should be unstable to the
production of charged pairs. We investigate the spontaneous production of such
Dyson pairs in electrodynamics coupled to gravity. They are found to consist of
pairs of zero-rest mass black holes with regular horizons. The properties of
these zero rest mass black holes are discussed. We also consider ways in which
a dilaton may be included and the relevance of this to recent ideas in string
theory. We discuss accelerating solutions and find that, in certain
circumstances, the `no strut' condition may be satisfied giving a regular
solution describing a pair of zero rest mass black holes accelerating away from
one another. We also study wormhole and tachyonic solutions and how they affect
the stability of the vacuum.
