Trapping of Nonlinear Gravitational Waves by Two-Fluid Systems

Abstract

We show that the coupled two-fluid gravitating system (e.g. stiff matter and 'vacuum energy') could trap nonlinear gravitational waves (e.g. Einstein-Rosen waves). The gravitational wave amplitude varies harmonically in time transferring the energy coherently to the stiff matter wave, and then the process goes to the backward direction. This process mimics the behaviour of trapped electromagnetic waves in two-level media. We have defined the limits for the frequency of this energy transfer oscillations. Investigation of the nonlinearly coupled state of electromagnetic waves with two or three level medium has become one of the hottest research spots this last decade 1,2,3 . The most exciting feature of this nonlinear effect is that the electromagnetic wave, which has a fixed propagation velocity in vacuum, could form with medium some breather-like structures localized in space. Such systems allows not only to slow down, and eventually stop 4 a light pulse 5,6,7 , but also there exists a possibility to release it, thus creating a gap soliton memory 8 . In the simplest case of two-level medium the governing equations are Maxwell-Bloch system 9,10 and, as the very recent theoretical investigations show 11 , one can control the mobility of the light pulse by the stationary radiation with a different polarization.We want to find out if similar effect exists for nonlinear gravitational waves inside of gravitating multi-component fluid systems, which are analogous to multilevel mediums in nonlinear optics.Existence of gravitational waves is generally accepted, at least since their indirect observation via energy and angular momentum losses in binary pulsars (see e.g. 12 and references therein). The study of gravitational waves involves mainly the weak field approximation of Einstein's equations (in close analogy with what is normally done in electromagnetism), which is obviously the relevant regime for 1

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