Absolute stability of Melvin's magnetic universe

Abstract

The physical structure of Melvin's magnetic universe is briefly examined and its dynamical behavior under arbitrarily large radial perturbations is discussed. It is shown that no radial perturbation can cause the magnetic field to undergo gravitational collapse to a singularity or electromagnetic explosion to infinite dispersion. Rather, when arbitrarily perturbed inside a finite region, the magnetic and gravitational fields undergo damped, turbulent oscillation until they have radiated away from the perturbed region all the energy associated with the perturbation. Then they settle down into Melvin's unperturbed, static configuration.