Gravitational two solitons in Levi-Civita spacetime

TL;DR

This paper constructs two-soliton solutions in Levi-Civita spacetime using inverse scattering, demonstrating that singularities can be removed and revealing nonlinear gravitational wave phenomena like soliton coalescence and splitting.

Contribution

It introduces a method to generate two-soliton solutions with cylindrical symmetry that can eliminate singularities, advancing understanding of gravitational wave interactions.

Findings

Singularities in the solutions can be removed by parameter tuning.

Solutions describe propagation of gravitational wave packets.

Observation of soliton coalescence and splitting phenomena.

Abstract

Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Civita solution as a seed, we construct a two-soliton solution with cylindrical symmetry. In our previous work, we constructed the one-soliton solution with a real pole and showed that the singularities that the Levi-Civita background has on an axis can be removed by the choice of certain special parameters, but it still has unavoidable null singularities, as usual one-solitons do. In this work, we show that for the two-soliton solutions, any singularities can be removed by suitable parameter-setting and such solutions describe the propagation of gravitational wave packets. Moreover, in terms of the two-soliton solutions, we mention a time shift phenomenon, the coalescence and the split of solitons as the nonlinear effect of gravitational waves.