Models of Static, Cylindrically Symmetric Solutions of the Einstein-Maxwell Field

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Abstract
Models of static, cylindrically symmetric solutions of the combined Einstein-Maxwell field equations are given. These models consist of extended distributions of matter with surface electric currents and magnetic fields outside the matter. The electric currents serve as sources of the magnetic fields; the distribution of matter as well as the magnetic fields serve as sources of the gravitational field. The magnetic lines of force may be parallel to the axis or circular and centered on the axis. The matter distribution is cylindrically symmetric and may be contained within a central cylinder or a tube centered about the axis. All ordinary physical and geometric requirements are satisfied by the models.

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