# An interpretation of spacetimes with expanding impulsive gravitational waves generated by snapped cosmic strings

## TL;DR

This paper analyzes the geometric structure of spacetimes with expanding impulsive gravitational waves generated by snapped cosmic strings, focusing on their construction, topology, and effects on test particles.

## Contribution

It provides a detailed review of the line element construction and complex mappings for these spacetimes, linking topology with physical effects on particles.

## Key findings

- Derived new complex mappings for various string configurations
- Connected spacetime topology with observable effects on test particles
- Enhanced understanding of global geometry of impulsive wave spacetimes

## Abstract

The geometric properties of spacetimes representing expanding impulsive gravitational waves, propagating on a flat background and generated by snapped cosmic strings, are studied. The construction of the line element is reviewed, and suitable forms of the string-generating complex mapping are derived for various configurations such as previously studied examples of a pair of snapping cosmic strings. Moreover, these mappings are related to the topology of the flat half-space in front of the wave. Their understanding seems to be crucial for further analysis of the global geometry, the relation between half-spaces on both sides of the impulse, and the physical interpretation of, in principle, observable effects. The spacetime structure is connected with the motion of free test particles crossing the impulse, where the recent results allow us to discuss their displacement and induced velocities that are caused by the interaction with the expanding gravitational impulsive wave.