Non-linear effects for cylindrical gravitational two-soliton

TL;DR

This paper investigates non-linear gravitational wave effects using a cylindrical two-soliton solution to Einstein's equations, highlighting phenomena like Faraday rotation, time shifts, and avoiding singularities present in single-soliton models.

Contribution

It constructs a new two-soliton solution with complex conjugate poles to study non-linear gravitational wave effects and avoids singularities inherent in single-soliton solutions.

Findings

Computed amplitudes of non-linear gravitational waves

Analyzed time dependence of wave polarizations

Demonstrated wave packet propagation at subluminal speeds

Abstract

Using a cylindrical soliton solution to the four-dimensional vacuum Einstein equation, we study non-linear effects of gravitational waves such as Faraday rotation and time shift phenomenon. In the previous work, we analyzed the single-soliton solution constructed by the Pomeransky's improved inverse scattering method. In this work, we construct a new two-soliton solution with complex conjugate poles, by which we can avoid light-cone singularities unavoidable in a single soliton case. In particular, we compute amplitudes of such non-linear gravitational waves and time-dependence of the polarizations. Furthermore, we consider the time shift phenomenon for soliton waves, which means that a wave packet can propagate at slower velocity than light.