Symmetry classes of pp-waves

Details Symmetry classes of pp-waves Symmetry classes of pp-waves

Dec 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986gregr..18.1229s&link_type=abstract

General Relativity and Gravitation (ISSN 0001-7701), vol. 18, Dec. 1986, p. 1229-1243.

Physics

17

Gravitational Waves, Relativity, Symmetry, Gauge Theory, Lie Groups, Tensors, Torsion

Scientific paper

The isometry groups admitted by plane-fronted gravitational waves with parallel rays are determined without use of any field equations. New groups with 5, 6, and 7 parameters arise which cannot occur for (nontrivial) exact solutions of Einstein's vacuum field equations. For all 17 possible cases the functional form of the free function in the metric is given. The classification is applied to Einstein-Maxwell fields, and a determination, in Riemann-Cartan geometry, of the form of the torsion tensor is obtained by assuming the vanishing of its Lie derivative with respect to the generators of the isometry groups.

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