Dyson Pairs and Zero-Mass Black Holes

TL;DR

This paper explores the theoretical possibility of Dyson pairs as zero-mass black holes in electrodynamics coupled with gravity, analyzing their properties, solutions, and implications for vacuum stability and string theory.

Contribution

It introduces the concept of zero-rest mass black holes as Dyson pairs, discusses their properties, and examines solutions including accelerating pairs, wormholes, and tachyonic configurations.

Findings

Zero rest mass black holes can form Dyson pairs with regular horizons.

Accelerating solutions satisfy the 'no strut' condition, indicating stable pair configurations.

Various solutions suggest potential effects on vacuum stability and connections to string theory.

Abstract

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.