Static cosmic strings in space–time with torsion, and strings with electromagnetism

Abstract

Cosmic strings are considered in space-time with torsion derived from a two-form potential, and in Minkowski space-time with electromagnetism. Using the curvature scalar as the geometrical part of the Lagrangian density, and the natural coupling to strings, the field equations are derived. It is shown a static string loop may satisfy the string equations of motion in the presence of an external torsion field. The gravitational field of the static string are derived in the weak field limit, and it is shown the gravitational field is repulsive exterior to the string. In Minkowski space-time, it is shown an external magnetic field can also give rise to a static loop.