Some Properties of Cylindrically Symmetric Einstein-Maxwell Fields

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Abstract
Some properties of static cylindrically symmetric universes consisting of gravitational and electromagnetic fields with a central axial mass, charge, or current density are discussed. Of three permissible distinct configurations, general solutions of the appropriate equations are given for two. The properties of the solutions of these two are then examined in greater detail. The equations of motion of test particles (both charged and uncharged) are described for some simple trajectories. The qualitative effect of the magnetic field on uncharged test particle behavior in some instances is noted as well as the qualitative distinction in the behavior of charged and uncharged test particles. The algebraically independent invariants of the Riemann tensor are calculated. A stability analysis is carried out for the two solutions when the system is subjected to radial perturbations. It turns out that both solutions are stable. The stability analysis is carried out by using the equations of the already unified field theory of Rainich, Misner, and Wheeler.

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