Strings and other distributional sources in general relativity

This paper deals with two broad issues: the formulation of a mathematical framework for concentrated sources in general relativity and its application to strings. We isolate a class of those metrics whose curvature tensors are well defined as distributions. It is shown that shells of matter: but neither point particles nor strings: can be described by metrics in this class. This conclusion is examined in more detail for the case of strings. We estimate the errors inherent in certain determinations of the mass per unit length of a cosmic string, and in certain calculations of the gravitational radiation from such a string.