Dyson pairs and zero mass black holes

It has been argued by Dyson in the context of QED in flat space-time 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.