Line sources in general relativity

This paper is a preliminary study of how the field of a thin massive "wire" can be characterized in general relativity. For a class of "simple" line sources, a linear stress-energy-momentum tensor can be defined in terms of the extrinsic curvature of a tube of constant geodesic radius centered on the wire, in the limit when the radius shrinks to zero. A number of examples are considered, including the ring singularity of the Kerr metric. The Kerr ring is composed of dustlike material circulating about it with the speed of light. The mass distribution in a cross section is proportional tc cos (2), where is the angle of rotation about the ring in a plane normal to it. The "half-pole" structure is compatible with single-valuedness because of the two-sheeted character of the Kerr manifold.