DYSON PAIRS AND ZERO MASS BLACK-HOLES

It has been argued by Dyson in the context of QED in flat space-time t hat 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 spo ntaneous production of such Dyson pairs in electrodynamics coupled to gravity. They are found to consist of pairs of zero rest mass black ho les with regular horizons, The properties of these zero rest mass blac k 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 circumstan ces, the ''no strut'' condition may be satisfied giving a regular solu tion 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.