# Construction and application of variations on the cylindrical gravitational waves of Weber, Wheeler, and Bonnor

## TL;DR

This paper constructs localized cylindrically symmetric gravitational wave solutions using harmonic mapping, revealing nonlinear mode conversions and their implications for Einstein gravity, with applications to Einstein-Maxwell systems.

## Contribution

It introduces a new method to generate localized cylindrical gravitational waves demonstrating nonlinear interactions and mode conversions, extending previous solutions.

## Key findings

- Localized waves exhibit strong mode conversion near the axis.
- Wave collisions induce mutual mode conversion.
- Solutions demonstrate genuine nonlinearity in Einstein gravity.

## Abstract

To clarify certain nonlinear properties of strong gravitational field, we investigate cylindrically symmetric gravitational waves that are localized as regular wave packets in the space of radial and time coordinates. The waves are constructed by applying a certain kind of harmonic mapping method to the seed solutions with linear polarization, which are generalizations of the solution representing a cylindrical gravitational pulse wave discussed by Weber-Wheeler and Bonnor. The solutions obtained here, though their form is rather simple, show occurrence of strong mutual conversion between a linear mode and a cross mode apparently. The single localized wave shows the conversion in the vicinity of the symmetric axis where the self-interaction is strengthened, and the collision between multiple waves also causes the conversion. These phenomena can be thought to be the emergence of genuine nonlinearity that the Einstein gravity holds. Finally we discuss a simple, but interesting application of the solutions to the case of the Einstein-Maxwell system.