On the dispersion of cylindrical impulsive gravitational waves

Details On the dispersion of cylindrical impulsive gravitational waves On the dispersion of cylindrical impulsive gravitational waves

Jul 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987rspsa.412...75c&link_type=abstract

Royal Society (London), Proceedings, Series A - Mathematical and Physical Sciences (ISSN 0080-4630), vol. 412, no. 1842, July 8,

Physics

4

Cylindrical Waves, Gravitational Waves, Wave Dispersion, Wave Packets, Einstein Equations, Reflected Waves, Scalars, Shock Discontinuity, Shock Fronts

Scientific paper

An exact solution, describing the dispersion of a wave packet of gravitational radiation, having initially (at time t = 0) an impulsive character, is analyzed. The impulsive character of the wave-packet derives from the space-time being flat, except at a particular radial distance at t = 0, and the time-derivative of the Weyl scalars exhibiting delta-function singularities at this radial distance, when t approaches 0. The principal feature of the dispersion is the development of a singularity of the metric function, nu, and of the Weyl scalar, Psi(2), when the wave, after reflection at the center, collides with the still incoming waves. The evolution of the metric functions and of the Weyl scalars, as the dispersion progresses, is illustrated graphically.

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