A snapping cosmic string in a de Sitter or anti-de Sitter universe

We present and describe an exact solution of Einstein’s equations which represents a snapping cosmic string in a vacuum background with a cosmological constant Λ. The snapping of the string generates an impulsive spherical gravitational wave which is a particular member of a known family of such waves. The global solution for all values of Λ is presented in various metric forms and interpreted geometrically. It is shown to represent the limit of a family of sandwich type N Robinson–Trautman waves. It is also derived as a limit of the C-metric with Λ, in which the acceleration of the pair of black holes becomes unbounded while their masses are scaled to zero.