Nonlinear effects for a cylindrical gravitational two-soliton

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.

Gravitational two solitons in Levi-Cività spacetime

“…Moreover, we have studied nonlinear effect of solitons such as a time shift phenomenon and the gravitational Faraday effect. We have seen that these effects are essentially similar to the case of d = 1, which was investigated in [14].…”

“…In addition to the time shift phenomena, when k q, physically and mathematically interesting phenomenon such as coalescence and split of solitons happens, as pointed out in [14]. As seen in Fig.…”

“…Here, [ ] denotes the real part of [ ]. When d = 1, we recover the metric in [14], in which case the seed is a Minkowski metric, and when c = 0, this metric reduces to the Levi-Cività metric. 1 The function ω can be rewritten in terms of X and Y as…”

“…(two-soliton solution obtained from Minkowski metric) have been previously analyzed by one of the authors [14]. This is why we focus on d = 3 (c I = 0) and d = 5 only in what follows.…”

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], 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.)…”