Superposition of Weyl solutions to the Einstein equations: cosmic strings and domain walls

Abstract

The solutions to the Einstein equations representing the superposition of a particle and a ring are studied. The appearance of strut-type and membrane-type singularities is analysed. These objects are compared with cosmic strings and domain walls. It is found that, unlike the usual domain walls, the membranes have null effective gravitational mass, as have struts and strings. The relationship of these membranes with walls associated with sigma-model-type field theories is indicated.