The collision and snapping of cosmic strings generating spherical impulsive gravitational waves

Abstract

The Penrose method for constructing spherical impulsive gravitational waves is investigated in detail, including alternative spatial sections and an arbitrary cosmological constant. The resulting waves include those that are generated by a snapping cosmic string. The method is used to construct an explicit exact solution of Einstein's equations describing the collision of two nonaligned cosmic strings in a Minkowski background which snap at their point of collision.

Cosmic branes and asymptotic structure

“…From the perspective of I + , a process in which a cosmic string is destroyed manifests as a transition from a metric on null hypersurfaces that has a deficit, to a metric that is a round sphere. Following the discussions in [29,54], we can match (3.1) and (3.2) on a null hypersurface at large r:…”

“…In [28], a physical interpretation of superrotations was given: it was argued that the poles in the meromorphic symmetry transformations are associated with cosmic strings piercing the celestial sphere. Indeed, meromorphic transformations on the celestial sphere were already discussed in the cosmic string literature, see [29] for a study of how the collision and snapping of cosmic strings generates gravitational waves. A physical motivation for allowing general enough boundary conditions for the asymptotic symmetry group to include superrotations is hence to ensure that one includes in the phase space solutions such as Robinson-Trautman and their impulsive limits (i.e.…”

“…In particular, in the derivations of [23] it is assumed that the only singularities in the complex plane are associated with infinity; singularities at finite points are more subtle and are considered. However, from the work [29], it is only possible to use conformal transformations to move all singularities to infinity in the complex plane when there is only a single cosmic string; in the presence of multiple cosmic strings not all of the singularities can be sent to infinity in the complex plane.…”

“…In section 3 we analyse the asymptotic behaviour of cosmic branes, focussing for definiteness on the example of cosmic membranes in five dimensions. Following analogous discussions to those in [28,29], we consider processes in which cosmic branes can snap, and infer the associated boundary conditions. In four dimensions, cosmic string snapping is consistent with asymptotically flat boundary conditions.…”

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

“…We will now use the Penrose "cut and paste" method [6] (see also [7], [12] and [13]) to construct an explicit solution representing a snapping cosmic string in a background with a non-zero cosmological constant. It is convenient to represent the (anti-)de Sitter background by a line element in the form ds 2 = 2 dU dV − 2 dη dη…”