Gravitational solitons in Levi-Civita spacetime

TL;DR

This paper constructs a cylindrically symmetric gravitational wave solution in vacuum Einstein's equations using inverse scattering, showing singularities can be removed and describing the wave's physical properties.

Contribution

It introduces a new single-soliton solution in Levi-Civita spacetime that models nonlinear cylindrical gravitational shock waves with singularities removable through parameter choices.

Findings

Singularities on the axis can be eliminated by parameter tuning.

The solution models nonlinear cylindrical gravitational shock waves.

Analysis of wave amplitudes and polarization angles provides physical insights.

Abstract

Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equation and using the Levi-Civita solution for a seed, we construct a cylindrically symmetric single-soliton solution. Although the Levi-Civita spacetime generally includes singularities on its axis of symmetry, it is shown that for the obtained single-soliton solution, such singularities can be removed by choice of certain special parameters. This single-soliton solution describes propagation of nonlinear cylindrical gravitational shock wave pulses rather than solitonic waves. By analyzing wave amplitudes and time-dependence of polarization angles, we provides physical description of the single-soliton solution.