Gravitational Waves in General Relativity. XII. Correspondence between Toroidal and Cylindrical Waves

Details Gravitational Waves in General Relativity. XII. Correspondence between Toroidal and Cylindrical Waves Gravitational Waves in General Relativity. XII. Correspondence between Toroidal and Cylindrical Waves

Feb 1972

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1972rspsa.327..123m&link_type=abstract

Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, Volume 327, Issue 1568, pp. 123-130

Physics

1

Scientific paper

A device making use of the linearity of one of the field equations for Rosen's cylindrically symmetric metric is employed to demonstrate a correspondence between some outgoing toroidal gravitational waves and imploding-exploding cylindrical waves. An exact form of axially symmetric metric for a smooth toroidal pulse in the region |z|t are considered. The solution remains valid throughout the reflexion of the wave as it meets itself on the symmetry axis, and displays this process clearly. As a particular example, a solution of Weber & Wheeler for a non-singular cylindrical pulse is converted into one for a time-symmetric toroidal pulse, and the distant field at the moment of time-symmetry is briefly examined.

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