Gravitational two solitons in Levi-Cività spacetime

Abstract

Applying the Pomeransky inverse scattering method to the four-dimensional vacuum Einstein equations and using the Levi-Cività 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-Cività 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.

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

“…To shed some new light on nonlinear features of gravitational waves, in previous works [10][11][12][13],…”

“…To shed some new light on nonlinear features of gravitational waves, in previous works [10][11][12][13], we studied cylindrically symmetric gravitational solitonic waves with nonaligned polarizations that are constructed on flat and Levi-Cività spacetime backgrounds by the inverse scattering method [14,15]. Through those studies, some interesting behaviors of the waves (time shift, gravitational Faraday effect, etc.)…”